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Popular Calculus >

y^{''}+4y=cos(x)cos(3x)

Solution

y^{^{''}} + 4 y = cos (x) cos (3 x)

Solution

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) cos ( x ) cos ( 3 x )}{2} d x + \frac{1}{2} (\frac{1}{2} cos (x) (sin (x) + \frac{1}{5} sin (5 x)) + \frac{1}{2} (\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{10} (\frac{1}{4} sin (4 x) - \frac{1}{6} sin (6 x)))) sin (2 x)

Solution steps

y^{''} (x) + 4 y = cos (x) cos (3 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) cos ( x ) cos ( 3 x )}{2} d x + \frac{1}{2} (\frac{1}{2} cos (x) (sin (x) + \frac{1}{5} sin (5 x)) + \frac{1}{2} (\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{10} (\frac{1}{4} sin (4 x) - \frac{1}{6} sin (6 x)))) sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) cos ( x ) cos ( 3 x )}{2} d x + \frac{1}{2} (\frac{1}{2} cos (x) (sin (x) + \frac{1}{5} sin (5 x)) + \frac{1}{2} (\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{10} (\frac{1}{4} sin (4 x) - \frac{1}{6} sin (6 x)))) sin (2 x)

Popular Examples

y^{''}+3y=-48t^2e^{3t}

solvefor d,d(t)=(100ln(t+2))/(t+2)

y^{''}-y^'=te^t,y(0)=2,y^'(0)=1

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4y=cos(x)cos(3x) ?
The solution for y^{''}+4y=cos(x)cos(3x) is