What is the solution for (d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x} ?

The solution for (d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x} is y=c_{1}e^{-7x}+c_{2}xe^{-7x}+1/36 e^{5x}

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(d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x}

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}

Solve linear ODE:

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

y^{^{''}} + 5 y^{^{'}} - y = 11

100 y^{^{''}} + 13 y^{^{'}} + \frac{6 y}{25} = 600

y^{^{''}} + y^{^{'}} - y = 2

y^{^{''}} + y^{^{'}} - 2 y = 4 e^{2 t}, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 3 y + 2 = 0

What is the solution for (d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x} ?
The solution for (d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x} is y=c_{1}e^{-7x}+c_{2}xe^{-7x}+1/36 e^{5x}