What is the solution for y^{''}-4y^'=7-3e^{4x} ?

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

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y^{''}-4y^'=7-3e^{4x}

y^{^{''}} - 4 y^{^{'}} = 7 - 3 e^{4 x}

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

Solution steps

y^{''} (x) - 4 y^{'} (x) = 7 - 3 e^{4 x}

Solve linear ODE:

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

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

x \to - π - lim ((x + π) csc (x))

ln^{5} (x)

\int \frac{2 x}{4 x ^{2} + 1} d x

\int \frac{1}{( 1 + y ^{2} )} d y

y = a x 1 - x

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