What is the solution for y^{''}-7y^'+10y=e^{3x}(-1+10x) ?

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

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y^{''}-7y^'+10y=e^{3x}(-1+10x)

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x} (- 1 + 10 x)

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

Solution steps

y^{''} (x) - 7 y^{'} (x) + 10 y = e^{3 x} (- 1 + 10 x)

Solve linear ODE:

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

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

(d^{3} - 3 d - 2) y = 540 x^{3} e - x

y^{^{''}} - 9 y^{^{'}} + 18 y = e^{6 t}

y^{^{''}} + y = 2 \cdot cos (x) \cdot cos (2 x)

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

y^{^{''}} + 4 y = - cos (3 t) - 2 sin (3 t)

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