What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x} ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x} is y=c_{1}e^{3x}+c_{2}e^{2x}+5xe^{3x}

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(d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 5 e^{3 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 5 e^{3 x}

Solve linear ODE:

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

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

\frac{( 10 s - 3 )}{s ^{2} + 4 s + 29}

\int \frac{x}{( 1 + 4 x ^{2} ) ^{2}} d x

f (x) = 4 x + 10

\frac{d}{d x} ((6 x + 7)^{2})

\int x^{2} \cdot ln^{2} (x) d x

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x} ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=5e^{3x} is y=c_{1}e^{3x}+c_{2}e^{2x}+5xe^{3x}