What is the solution for (d^2y)/(dx^2)-10*(dy)/(dx)+25*y=30*x+3 ?

The solution for (d^2y)/(dx^2)-10*(dy)/(dx)+25*y=30*x+3 is y=c_{1}e^{5x}+c_{2}xe^{5x}+(6x)/5+3/5

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(d^2y)/(dx^2)-10(dy)/(dx)+25y=30*x+3

\frac{d ^{2} y}{d x ^{2}} - 10 \cdot \frac{d y}{d x} + 25 \cdot y = 30 \cdot x + 3

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{6 x}{5} + \frac{3}{5}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 10 \cdot \frac{d y}{d x} + 25 \cdot y = 30 \cdot x + 3

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{6 x}{5} + \frac{3}{5}

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{6 x}{5} + \frac{3}{5}

y^{^{''}} - 5 y^{^{'}} = 28 x e^{- 2 x} + 10

y^{^{''}} - 9 y^{^{'}} + 20 y = 6 x + e^{4 x}

y^{^{''}} + 9 y = 16 sin (3 x) + 12 cos (3 x)

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 10 sin (t)

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 e^{5} t

What is the solution for (d^2y)/(dx^2)-10*(dy)/(dx)+25*y=30*x+3 ?
The solution for (d^2y)/(dx^2)-10*(dy)/(dx)+25*y=30*x+3 is y=c_{1}e^{5x}+c_{2}xe^{5x}+(6x)/5+3/5