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Popular >

y^{''}-4y=8x

Solution

y^{^{''}} - 4 y = 8 x

Solution

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

Solution steps

y^{''} (x) - 4 y = 8 x

Solve linear ODE:

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

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

Graph

Popular Examples

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y^{^{''}} + 9 y = cos (x)

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y^{''}+3y^'-4y=(x^3+x)e^x

y^{^{''}} + 3 y^{^{'}} - 4 y = (x^{3} + x) e^{x}

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y^{^{''}} - 5 y^{^{'}} + 6 y = 3 e^{3 x} + 36 x^{2}

x^{''}+16x=8sin(2t)

x^{^{''}} + 16 x = 8 sin (2 t)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-4y=8x ?
The solution for y^{''}-4y=8x is y=c_{1}e^{2x}+c_{2}e^{-2x}-2x