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Popular >

y^{''}-2y+y=x

Solution

y^{^{''}} - 2 y + y = x

Solution

y = c_{1} e^{x} + c_{2} e^{- x} - x

Solution steps

y^{''} (x) - 2 y + y = x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - x

y = c_{1} e^{x} + c_{2} e^{- x} - x

Graph

Popular Examples

y^{''}+100y=3cos(8t),y(0)=0,y^'(0)=0

y^{^{''}} + 100 y = 3 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{''}+2y^'=-sin(x)

y^{^{''}} + 2 y^{^{'}} = - sin (x)

y^{''}-4y^'+4y=-3+2x+2x^2

y^{^{''}} - 4 y^{^{'}} + 4 y = - 3 + 2 x + 2 x^{2}

y^{''}-9y=sin(2x)

y^{^{''}} - 9 y = sin (2 x)

(d^2y)/(dx^2)+y=32x^3

\frac{d ^{2} y}{d x ^{2}} + y = 32 x^{3}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-2y+y=x ?
The solution for y^{''}-2y+y=x is y=c_{1}e^x+c_{2}e^{-x}-x