What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x) ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x) is y=c_{1}e^{4x}+c_{2}-6/5 sin(2x)-3/5 cos(2x)

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(d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 12 cos (2 x)

y = c_{1} e^{4 x} + c_{2} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 12 cos (2 x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

y = c_{1} e^{4 x} + c_{2} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

\int \frac{6 - 6 x}{1 - x} d x

y = 3 x^{2} + 1, (0, - 1)

y^{^{''}} - 7 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

(5, - 4), (4, 7)

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x) ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x) is y=c_{1}e^{4x}+c_{2}-6/5 sin(2x)-3/5 cos(2x)