The general solution of the 3rd order equation y′′′ − y′ = 0 is given by y(x) = C1x + C2e^x + C3e^−x.

Q: Each of the following equations represents a cubic function

A: Given data: The first equation is y=2x2+3. The second equation is y=-x1/2-1. The third equation is…

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: Solve: x'y" - 7xy' + 41y =0

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Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

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Q: Determine all solutions. y'= (x-y + 3)²

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Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: 2.x²y"+xy'–3y= 0,x>0

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Q: The general solution of y' x2 can be written in the form

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Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: (2x + 3)y' = y + √2x + 3, when x = -1, y = 0.

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Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

A: The given differential equation is a second order differential equation so we will first reduce its…

Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

Q: y" + 2y'-3y 7x-3x.

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Q: Solve x'y-5xy+13y-0

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Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: Example 4: Solve iii) y" + 2y' – 3y = 7x – 3x?. -

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Q: 3) y +2/u

A: Given: y+2y=x

Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

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Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

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Q: y(1) + 2y"" + y"+ 2y' = xe-2x

A: Here we use one method of linear differential equations with constant coefficients. i.e. The…

Q: Solve :     x²y"-2x(1+x)y'+2(1+x)y = x3

A: Given: The second order differential equation is x2y''-2xx+1y'+2x+1y=0