Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: What is the particular solution to the differential equation = (x – 1)(1 y) with the initial…

A: givendydx=(x-1)(1-y)we will solve this equation by Variable separable method

Q: Solve the separable differential equation dy 7x – 6yVx² +1 = 0. - dx Subject to the initial…

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Q: Find the differential equation such that y(x) = c,(x– 1) 2+czln(x – 1)(x– 1)

A: we will eliminate the variables by differentiating

Q: Solve the differential equation with initial condition dy 7y²x3 dx %3D У (2) %3D 3

A: The main objective of the question is to establish relation between x and y.

Q: Find the general solution for differential equation.

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Q: Find the general solution for differential equation.

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Q: 1. Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: (D² – 3D + 2) y = (1+e-*)?

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: The given differential equation can be solved by the variable separable method. first, separate the…

Q: Solve the differential equation dy/dx =x/y2 with initial condition y(0) = 2.

A: Given : dydx = xy2

Q: Find the complete solution of the differential equation dy dy +3 dx - 5y = e-2X sin2x dx?

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Q: Find the general solution for differential equation.

A: Given differential equation is dydx+2xy=16x. Separate the variable.…

Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

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Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.

A: We have to verify the solution

Q: Find the general solution of the ordinary differential equation: r²y" – ry + y %3D

A: The differential equation is given as x2y''-xy'+y=2x                         (1) It is a Cauchy…

Q: Find the general solution for differential equation.

A: Given differential equation is xdydx+2xy-x2=0. To find the general solution of the given…

Q: d. 2ydx +x(x² In y – 1)dy = 0 -

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Q: Solve the differential equation for y. 2 dy d²y ey dx. dx² 3%. =

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Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

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Q: Find the general solution for differential equation.

A: To find the general solution: dydx+4xy=4x Solution: dydx+4xy=4x On simplifying further we get:…

Q: Find a second solution of each differential equation. x²y" + xy' + y = 0; y1 = cos (In x). (1+x)y" +…

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Q: Verify that the function y (x) = ln (x + c) is a solution of the differential equation e^y y` = 1…

A: The given differential equation is: ey y'=1

Q: 2x³y' = y(y² + 3x?)

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Q: Find the solution of the differential equation (In(y))³ dy dx = x'y 3 which satisfies the initial…

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Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

Q: Find the general solution of differential equation dy/dx = (y^2x + x^3)/(x^3-x^2y)

A: We need to solve dydx=y2x+x3x3-x2y. So,              dydx=y2x+x3x3-x2ySubstitute  dydx with y'.⇒y'…

Q: Verify that y = c, sin 3x + c2 cos 3x + 4e* is a solution to the differential equation y"-y" + 3y'-…

A: We have to verify that, y = c_1 sin 3x + c_2 cos 3x + 4e^x ;  is a solution to the differential…

Q: Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2…

A: Given- dydx+1xy=6x+2 To find- the general solution of the above first order differential equation.…

Q: 3a. Verify that both yı(x) = 0 and y2(x) = (x – 2)ª %3D are solutions to the differential equation…

A: 3a.To verify that both  y1(x)=0 and y2(x)=(x-2)3 are the solutions of the differential…

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: Solve the differential equation. dy Y- (In x)4 dx A y =x (In x) 5 + cx B y= ! x5 + cx y = = x (In x)…

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Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

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Q: Solve the Euler-Cauchy differential equation dy -3x + 4y = dx In?x - Inx

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Q: Find the solution of the differential equation dy = cos(5x) Vy dx which satisfies the initial…

A: y'=cos5xy dydx=cos5xy dyy=cos5xdx y-12dy=cos5xdx take integration

Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

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Q: Show that the differential equation dy / dx = y / x is inexact and that a factor of 1 / x ^ 2 can…

A: Given differential equation is, dydx=yx.

Q: Show that the function y=ex(sin2x+cos2x) is a solution of the differential equationy′′−2y′+5y=0.

A: We find the first two derivatives of y using the product rule

Q: e. xy' – y = x*y"

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Q: Solve the differential equation dy dx 3y3 1 %3D By the method of separating the variables

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Q: Find the particular solution of the differential equation dy (x – 8)e-2y dx | satisfying the initial…

A: W can solve the given differential equation by using the variable separable method.Then apply the…

Q: The particular solution of the differential equation: y" + 3y' + 2y = sin(e*) %3D is:

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Q: Solve the differential equation dy 1 dx 3y3 By the method of separating the variables

A: Answer is in below step.

Q: Solve the Euler-Cauchy differential equation dy - 3x +4 y = In ² x – In x xp dx

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Q: Show that (y^2-1)^2=Ax is the general solution of the differential equation 4xy dy/dx =-1+y^2.

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Q: 2(2x? + у?)dx — ху dy %3D 0

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Q: Show that y1 =- and y2 = Vx are solutions of the following differential equation 4x3у" + 7x?у' — ху…

A: According to the given information, it is required to show that the given y1 and y2 are the…

Q: | Find the solution of the differential equation (In(y))³ dy = x'y dx which satisfies the initial…

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Q: Solve the differential equation: dy 1 1 1)y – x +1 = 0, y1= ax - - dx

A: The given differential equation is dydx-y2x-21x-1y-x+1=0. Substitute y=ax in the above equation and…