What is the solution for y^{''}-7y^'+10y=6x+e^{2x} ?

The solution for y^{''}-7y^'+10y=6x+e^{2x} is y=c_{1}e^{5x}+c_{2}e^{2x}+(3x)/5+21/50-(e^{2x}x)/3

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y^{''}-7y^'+10y=6x+e^{2x}

y^{^{''}} - 7 y^{^{'}} + 10 y = 6 x + e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{2 x} + \frac{3 x}{5} + \frac{21}{50} - \frac{e ^{2 x} x}{3}

Solution steps

y^{''} (x) - 7 y^{'} (x) + 10 y = 6 x + e^{2 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{2 x} + \frac{3 x}{5} + \frac{21}{50} - \frac{e ^{2 x} x}{3}

y = c_{1} e^{5 x} + c_{2} e^{2 x} + \frac{3 x}{5} + \frac{21}{50} - \frac{e ^{2 x} x}{3}

4 y^{^{''}} - 2 y^{^{'}} = 4 x, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} - 12 y = (4 x + 7) e^{- 2 x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{3 x}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 6 e^{2 x} + 16 x^{2}

y^{^{''}} + 4 y = \frac{3}{sin ( 2 x )}

What is the solution for y^{''}-7y^'+10y=6x+e^{2x} ?
The solution for y^{''}-7y^'+10y=6x+e^{2x} is y=c_{1}e^{5x}+c_{2}e^{2x}+(3x)/5+21/50-(e^{2x}x)/3