What is the solution for y^{''}-7y^'=5x*e^x ?

The solution for y^{''}-7y^'=5x*e^x is y=c_{1}e^{7x}+c_{2}-(5e^xx)/6+25/36 e^x

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y^{''}-7y^'=5x*e^x

y^{^{''}} - 7 y^{^{'}} = 5 x \cdot e^{x}

y = c_{1} e^{7 x} + c_{2} - \frac{5 e ^{x} x}{6} + \frac{25}{36} e^{x}

Solution steps

y^{''} (x) - 7 y^{'} (x) = 5 x \cdot e^{x}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} - \frac{5 e ^{x} x}{6} + \frac{25}{36} e^{x}

y = c_{1} e^{7 x} + c_{2} - \frac{5 e ^{x} x}{6} + \frac{25}{36} e^{x}

What is the solution for y^{''}-7y^'=5x*e^x ?
The solution for y^{''}-7y^'=5x*e^x is y=c_{1}e^{7x}+c_{2}-(5e^xx)/6+25/36 e^x