en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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^{''}-y^'-2y=3e^{2x}

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x}

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

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

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

d, d (t) = \frac{100 ln ( t + 2 )}{t + 2}

y^{''}-3y^'+2y=3e^{-x}-10cos(3x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 e^{- x} - 10 cos (3 x)

y^{''}-81y=sinh(9x)

y^{^{''}} - 81 y = sinh (9 x)

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