What is the solution for y^{''}-5y^'+6e^x=0 ?

The solution for y^{''}-5y^'+6e^x=0 is y=c_{1}e^{5x}+c_{2}+3/2 e^x

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y^{''}-5y^'+6e^x=0

y^{^{''}} - 5 y^{^{'}} + 6 e^{x} = 0

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 e^{x} = 0

Solve linear ODE:

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

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

What is the solution for y^{''}-5y^'+6e^x=0 ?
The solution for y^{''}-5y^'+6e^x=0 is y=c_{1}e^{5x}+c_{2}+3/2 e^x