Find f(x) where we cannot solve for f'(x) = 0, but f(x) cannot be = 1/x

Q: Determine whether the given function is a solution to the given differential equation. y = sin x…

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Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: Find the particular solution that satisfies the differential equation and the initial condition. f…

A: We know,  f(x) = ∫f'(x) dx

Q: The solution to differential equation associated with the path taken by a projectile for which the…

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Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

A: F(X)= 12x3 +3CSC2X- 5√x - 4π   ∫F(x) dx = ?   Important points: 1. ∫xndx = xn+1n+1 + c2. ∫cosec2x =…

Q: d) sin(x)y' + cos(x)y = tan(x)

A: We have to solve

Q: obtain the differential equation of: Circles with center on the line y = -x and passing through the…

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Q: Find the particular solution that satisfies the differential equation and the initial condition. f…

A: ddxf(x) = f'(x)f(x) = ∫f'(x) dx

Q: y using an integrating factor, find the general solution of the differential equation dy/dx…

A: Given differential equation :                          dydx-ytanx=sinx

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: A toxic chemical accidentally released into the environment from a metal processing plant degrades…

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Q: Consider the differential equation y"+ya+x. If g(x) is a solution of the differential equation…

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Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: Based on a function, try to construct a non-homogenous differential equation with at least 2nd order…

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Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

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Q: ① Solveing dy - - x dx = 。 ㅎ

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Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: y In(x) ln(y)dx + dy

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Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y = "

A: The given differential equation is solved below in detail.

Q: Find the differential equation of the family of cuves and draw at least three members of the family…

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Q: 1. finol Solution of the differential equatiou

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Q: Use integration to find a general solution of the differential equation

A: Given: dydx = xex2  To find: General solution of the given differential equation.

Q: Find the differential equation of family of circles tangent to the x-axis.

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Q: The _______ of a differential equation is the power of the highest orfer derivative term in the…

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Q: obtained in factored form a linear differential equation with real constant coeffiecients that…

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Q: Prove first that sinx siny dx - cosx cosy dy =0 is an exact differential equation then determine its…

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Q: Find the differential equation (Eliminating Arbitrary Constant)(Family of Curves): Strophoids :…

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Q: Find the particular solution that satisfies the differential equation and the initial condition. f…

A: The explanation of the solution as follows:

Q: What is the appropriate μ(x) integration factor of the equal linear differential equation?…

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: when we determine the highest derivative in a differential equation, we are actually determining the…

A: According to the question, we have to check the statement either it is true or false and the…

Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) = c₁cos(x) +…

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Q: Find general solution of differential equation. Enter transient terms if any. x^2y' + xy= 7

A: Here we will find out the required general solution for given differential equation.

Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

Q: Obtain the differential equation for the family of straight lines with x-intercept and y-intercept…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: Find the ordinary differential equation of a circle which passes through the points (0,0) and (2,0).

A: We will find out the required differential equation for given circle.

Q: Solve for Higher Differential Equation using Variation of Parameters et x" – 4x' + 3x 1+et

A: see below the answer  as per bertleby I have to solve first question only, please resubmit for other…

Q: dy – (x - y + 1)?dx = 0

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Q: 2. Obtain the differential equation having the solution as the equation representing all circles of…

A: The solution is given as

Q: Find the differential equation of all family of circles in which the center lies on the line y = -x…

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Q: An integrating factor for the linear differential equation = x - is (Select the correct answer.) x2…

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Q: Use variation of parameters to solve the differential equation x²y" + y = x. [Leave u₁ and u₂ in…

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Q: Show that OW

A: x2+y2-xdx-ydy=0x2+y2-xdx+-ydy=0                 -Equation1Let M=x2+y2-x and N=-y∂M∂y=2y , ∂N∂x=0As…

Q: In a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground…

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: Find the particular solution that satisfies the differential equation and the initial condition.   f…

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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.