Find the general solution of the first-order differential equation for  x > 0  by any appropriate method. (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) y' = 70x6 Square root1-y2

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

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Q: the 2nd order of the non-homogeneous differential equation, y''-y'-6y=4xex using methods of…

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Q: 3. For the below ordinary differential equation with initial conditions, state the order and…

A: Given differential equation x2y2-3dydx=12y  y(1)=2. The objective is to solve the differential…

Q: Find the general solution of the differential equation. (Use C for any needed constant.) y' = 10VX y…

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Q: determine the general solution to thegiven differential equation. Derive your trial solution…

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Q: Find a particular solution Y of the nonhomogeneous differential equation y 00 + y 0 + y = 2 cost −…

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Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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Q: Solve the differential equation with appropriate method. Express final answer free of fractions and…

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Q: The diffeterctial equation is y²dx+ 3xZy² dx + dy=0

A: In the given question we have to find the value of the constant c at the point (2,1) when we solve…

Q: The solution of the differential equation using variable separable  dydx+7secy=

A: To find the solution of differential equation dy/dx+7secy=0

Q: An object of mass m falls from rest and its velocity v given by dv =mg - kv v(0) =0 dt -- where k is…

A: Consider the given equation. mdvdt=mg-kv Further, simplify and make for integration.…

Q: The solution of the given differential equation for y(1.5) is h=0.1 interval value. Calculate by…

A: Euler's method uses the formula, yn+1=yn+hf(xn,yn) to perform the iterations.

Q: find the general solution of the first-order linear differential equation. y' + y = ex

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Q: the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: (x² + y²)dx – xydy = 0 %3D -

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Q: y' - y = 2x? 3

A: Given:   y' - 3xy = 2 x2   To Find: An explicit solution of the above differential equation by…

Q: Solve the general solution of the second order linear differential equation with constant…

A: rewriting the equation we get  y'-1t2-1y2=-1t2-1

Q: Determine the values of r for which the differential equation y'-y = 0, has a solution of the y =…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: The given differential equation is, y''+2y'-8y=5e-2x-e-x. Obtain the homogeneous solution.…

Q: μ (x, y)=xayb and find the general solution to the equation

A: Here we have to find out both integrating factor and general solution.

Q: y" + 2 y' + y =

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Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: Using Euler's method, compute y (0-5) for differential equation =y -x, with y =1 when x=0

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Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: Differential Equation x(y+2)+y'=0  Initial Condition y=-8 when x=0

Q: Determine the value of C for the given first order differential equation when x-2 and y=1. e#+v/ =…

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Q: Find the general solution of the first-order differential equation                       y′ cos x2 +…

A: The first-order differential equation is y'cosx2+ycosx2x=secx2

Q: Find the (real-valued) general solution to the differential equation. z′′+7z′=0 (Use constants A,…

A: To Find the (real-valued) general solution to the differential equation. z′′+7z′=0

Q: The integrating factor of non-exact differential equation (x°y³ – ®)dx – (y6 – x³y)dy = 0 - -

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Q: Obtain the general solution of the given differential equation using the appropriate method. y' = y…

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Q: Form the differential equation whose solution is y = c1cosz + c2sinx Also find the particular…

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Q: Consider the Non-Homogenous differential equation: y"-y= 6sinx Given that y. = Ce* + Cze-*, using…

A: Suppose we have second order linear differential equation as .  Consider are independent solutions…

Q: y" -y'-zy= 4et

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A: Given query is to find the solution of the differential equations provided.

Q: 1 y" + 3 y' + 2 y 1+ et

A: Given differential equation is as below:

Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y ae" + be-ª.

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: From the differential equation by eliminating the arbitary constant A and B from the equation y = e*…

A: The objective is to form the differential equation by eliminating the arbitrary constant A and B…

Q: Use the initial condition to find the particular solution of the differential equation. differential…

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Q: Consider the nonhomogeneous second order differential equation a°y" – xy' + y = nT +0, x > 1.

A: First we have to find the general solution of the differential equation x2y''-xy'+y=xlnx where x≠0,…

Q: Find the equilibrium point(s) for the differential equation y" =y - y2 and determine their stability

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Q: Find the particular solution of the differential equation satisfying the initial condition…

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Q: Find particular solution of the differential equation dydx-2x+13=4x+1y , given x=0, when y=0

A: I have solved using integrating factor

Q: y' = ycotx + y²cscx

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = aeª +…

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Q: For the differential equation y" --y' --= 0, find a particular solution which satisfies the initial…

A: To find the particular solution for the given differential equation which satisfies the initial…

Q: Find the linear homogeneous differential equation with constant coefficients and the general…

A: Given the solution is y=2+3x-4x2e4x+e4x   NOTE: If Auxiliary equation of a differential equation…

Q: For differential equation y'=t(y2 + 1) is the differential equation autonomous and does it have…

A: Given,  y'=t(y2+1)  If a differential equation is of the form y'=f(y) then it is called autonomous…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.