1. A particle moves along the x-axis according to the equation x=2r+3F, where x is in m and is in second. Calculate the instantaneous velocity and instantaneous acceleration at =3s.

Q: Sketch some slope lines for the differential equation problem dy/dt = t^3 and brieflysketch the…

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Q: E. Solve tne differential Equotions ☺ Czxy + xln3x)dy + .(xtyJ dx =0 when x =3, y=2

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Q: 3.u 3.Use differentials to approximate the value of v99.4

A: In this question we have to find the approximation value of 99.4

Q: Q.5.Suppose that a projectile is launched straight upwad from the initial position with initial…

A: Given data:- The given initial velocity, v0>0 The given differential equation, dvdt=-g1+ρgv2…

Q: 14. A particle moves along the x-axis so that its acceleration at any time t is a(t) = 2t - 7. If…

A: Given that, A particle is moving along the x-axis so that its acceleration at time t is a(t) = 2t…

Q: Provided the integrating factor (IF) = xy2, find the general soution of the differential equation…

A: Multiply the integrating factor in the differential equation to make it exact.

Q: Solve the following differential equation using variation of parameter. 4y" – y = xe"/2; y(0) = 1,…

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Q: dy Write down a differential equation of the form dt solutions all approach y = as t- →8. y' = = 78…

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Q: Solve the differential equatons (7x-ty +16) dy + (2x-5y+12) dx=o when x-3, y= 2

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Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: dy Write down a differential equation of the form dt all other solutions diverge from y = 8 as t →…

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Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: Find the solution to the differential equation dz = 2te?z dt at passes through the origin.

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Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: Show that y = x³ – x² +5 (where C is a constant) is a solution of the differential x y" + 2y' =…

A: Differentiating with respect to x, we get

Q: A spring attached to the ceiling is stretched 1,225 meters by a one kilogram mass. If the mass is…

A: The differential equation for the position x of the mass m of the spring mass system with mass m,…

Q: dy Write down a differential equation of the form =ay + b whose dt 7 solutions all approach y = 8 y'…

A: What is Differential Equation: A differential equation is an equation involving the terms of…

Q: dy Write down a differential equation of the form ay +b whose dt all other solutions diverge from y…

A: It is required to find a differential equation of the form dydt=ay+b. whose all other solutions…

Q: Consider the second-order differential equation + 25y = 4.5 sin(8t). d²y dt² Find the Particular…

A: The given problem is solved below in detail.

Q: dy Write down a differential equation of the form dt all other solutions diverge from y = 4 as t →∞.…

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Q: Compute for the initial velocity of 3÷(cos(45)×38. Show your complete solution

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Q: A direction field of the differential equation y= y – e² is given as follows: Select one: O True O…

A: The direction filed given if FALSE

Q: (64 – 2) dy = 1, y(0) = 9 Solve the initial-value problem for y as a function of x. %3D da

A: We need to solve the initial-value problem 64-x2 dydx=1, y0=9 for y as a function of x. So,…

Q: The differential equation corresponds to Newton's law of cooling is O a. dT L = k(M – T) dt O b. OY…

A: According to the given information, it is required to select the correct option.

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: QUESTION 4 Given f(x) = 8x3 + 2x. Estimate the value of f(2.01) using differential.

A: Given that: f(x)=8x3+2x

Q: (9 – 2²) dy = 1, y(0) = 9 Solve the initial-value problem for y as a function of r. %3D dx

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Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

Q: Write down a differential equation of the form = ay + b whose ay dt all other solutions diverge from…

A: We have to determine a differential equation of the form dydt=ay+b. The solution of differential…

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: Differential equations

Q: 3.A mass of 100 g stretches a spring 5 cm. If the mass is set in motion from its equilibrium…

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Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: dy Plot the slope field for the differential equation dx = y?- - x and sketch the solution for the…

A: Solution is given below:

Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). * y = In(e* + e4r) 2y +…

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Q: 16. Use differentials (that is, linear approximation) to approximate: V3.9 – e0.05

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Q: The differential equation corresponds to Newton's law of cooling is dT а. = k(T – M) dt O b. dT =…

A: Newton's law of cooling stats that cooling rate of a heated body is directly proportional to…

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Consider the function y=4e^rx+7 where r is some real number. If y satisfies the differential…

A: In this question we have to find the value of r.

Q: dy ay + b whose dt Write down a differential equation of the form all other solutions diverge from y…

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Q: Draw a slope field for the differential equation V = 0.21² + y and sketch an approximate solution…

A: Given differential equation is y'=0.2x2+y

Q: dy = ay + b whose dt Write down a differential equation of the form all other solutions diverge from…

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Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

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Q: Find the general solution of the given higher-order differential equatio y(4) + у" + y" %3D 0 y(x)…

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Q: dy Write down a differential equation of the form dt all other solutions diverge from y 9 as t →∞. =…

A: The differential equation has a form dydt=ay+b whose all other solutions diverge from y = 9 as t→∞

Q: 3. A model for the velocity v at time t of a certain object falling under the influence of gravity…

A: The equation of the certain object in viscous medium is given by dv/dt = 1 - v/8

Q: Solve the initial-value problem for y as a function of x. (25−x^2)dy/dx=1, y(0)=9 y=?

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Q: dy Write down a differential equation of the form dt solutions all approach y as t→∞. y' = 78 = ay +…

A: It is given that y=78 as t→∞. The objective is to find the differential equations of the form…