What is the solution for derivative of (dy/(dx))+4y=2sin(2x) ?

The solution for derivative of (dy/(dx))+4y=2sin(2x) is y=c_{1}cos(2x)+c_{2}sin(2x)-(xcos(2x))/2

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derivative of (dy/(dx))+4y=2sin(2x)

\frac{d}{d x} (\frac{d y}{d x}) + 4 y = 2 sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x cos ( 2 x )}{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = 2 sin (2 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x cos ( 2 x )}{2}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x cos ( 2 x )}{2}

2 x^{^{''}} + 12 x^{^{'}} + 50 x = 0

80 \cdot 2 2^{\frac{t}{20}}

\int \frac{6}{9 + 6 x} d x

\frac{d}{d x} (sin (2 x) + cos (3 x))

f (x) = π^{3 x + 3}, at x = 2

What is the solution for derivative of (dy/(dx))+4y=2sin(2x) ?
The solution for derivative of (dy/(dx))+4y=2sin(2x) is y=c_{1}cos(2x)+c_{2}sin(2x)-(xcos(2x))/2