What is the solution for 2y^{''}-7y^'+3y=5e^{2x} ?

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

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2y^{''}-7y^'+3y=5e^{2x}

2 y^{^{''}} - 7 y^{^{'}} + 3 y = 5 e^{2 x}

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

Solution steps

2 y^{''} (x) - 7 y^{'} (x) + 3 y = 5 e^{2 x}

Solve linear ODE:

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

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

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