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Popular >

y^{''}+4y^'+4y=x^2e^{-2x}+1

Solution

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} e^{- 2 x} + 1

Solution

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{4}}{12} + \frac{1}{4}

Solution steps

y^{''} (x) + 4 y^{'} (x) + 4 y = x^{2} e^{- 2 x} + 1

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{4}}{12} + \frac{1}{4}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{e ^{- 2 x} x ^{4}}{12} + \frac{1}{4}

Popular Examples

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

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

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

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

y^{''}-2y^'-3y=4e^x-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 6

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

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

y^{''}+36y=24cos(6x)-12sin(6x)

y^{^{''}} + 36 y = 24 cos (6 x) - 12 sin (6 x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4y^'+4y=x^2e^{-2x}+1 ?
The solution for y^{''}+4y^'+4y=x^2e^{-2x}+1 is y=c_{1}e^{-2x}+c_{2}xe^{-2x}+(e^{-2x}x^4)/(12)+1/4