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Popular >

y^{''}-y-x=0

Solution

y^{^{''}} - y - x = 0

Solution

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

Solution steps

y^{''} (x) - y - x = 0

Solve linear ODE:

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

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

Popular Examples

(D^2+2)y=e^{x+2}

(D^{2} + 2) y = e^{x + 2}

(D^2-4D+4)y=e^x+x^2+cos(2x)

(D^{2} - 4 D + 4) y = e^{x} + x^{2} + cos (2 x)

y^{''}+2y^'+2y=(t-pi),y(0)=2,y^'(0)=1

y^{^{''}} + 2 y^{^{'}} + 2 y = (t - π), y (0) = 2, y^{^{'}} (0) = 1

y^{''}+8y^'+17y=2e^{-4t}cos(t)

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 4 t} cos (t)

y^{''}-8y^'+20y=100x^2+26xe^x

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-y-x=0 ?
The solution for y^{''}-y-x=0 is y=c_{1}e^x+c_{2}e^{-x}-x