What is the solution for y^{''}+4y^'-21y=5e^{2x}+4 ?

The solution for y^{''}+4y^'-21y=5e^{2x}+4 is y=c_{1}e^{3x}+c_{2}e^{-7x}-5/9 e^{2x}-4/21

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y^{''}+4y^'-21y=5e^{2x}+4

y^{^{''}} + 4 y^{^{'}} - 21 y = 5 e^{2 x} + 4

y = c_{1} e^{3 x} + c_{2} e^{- 7 x} - \frac{5}{9} e^{2 x} - \frac{4}{21}

Solution steps

y^{''} (x) + 4 y^{'} (x) - 21 y = 5 e^{2 x} + 4

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 7 x} - \frac{5}{9} e^{2 x} - \frac{4}{21}

y = c_{1} e^{3 x} + c_{2} e^{- 7 x} - \frac{5}{9} e^{2 x} - \frac{4}{21}

y^{^{''}} + 4 y = 1 - t^{3}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = sin (2 x)

y^{^{''}} + y = sin^{2} (t)

y^{^{''}} + 4 y^{^{'}} + 4 y = 1 + x - 7 e^{- 2 x}

y^{^{''}} + 4 y = cos (3 t)

What is the solution for y^{''}+4y^'-21y=5e^{2x}+4 ?
The solution for y^{''}+4y^'-21y=5e^{2x}+4 is y=c_{1}e^{3x}+c_{2}e^{-7x}-5/9 e^{2x}-4/21