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Popular >

y^{''}-9y=x

Solution

y^{^{''}} - 9 y = x

Solution

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x}{9}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x}{9}

Popular Examples

y^{^{''}} + y = 2 \cdot e^{x}

y^{''}-y^'-6y=10xe^{3x}+17e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = 10 x e^{3 x} + 17 e^{3 x}

y^{''}-4y=x+sin(x)

y^{^{''}} - 4 y = x + sin (x)

y^{''}-4y^'+4y=e^xsin(x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x} sin (x)

y^{''}-4y^'+5y=10x^2+4x+8

y^{^{''}} - 4 y^{^{'}} + 5 y = 10 x^{2} + 4 x + 8

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-9y=x ?
The solution for y^{''}-9y=x is y=c_{1}e^{3x}+c_{2}e^{-3x}-x/9