What is the solution for y^{''}+6y^'-7y=3e^{2x}-2e^{3x} ?

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

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y^{''}+6y^'-7y=3e^{2x}-2e^{3x}

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) - 7 y = 3 e^{2 x} - 2 e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

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