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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

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

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

y^{''}+y=3sec(t)

y^{^{''}} + y = 3 sec (t)

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

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

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

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

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

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

Frequently Asked Questions (FAQ)

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