What is the solution for y^{''}+y=sin(t)+cos(t) ?

The solution for y^{''}+y=sin(t)+cos(t) is y=c_{1}cos(t)+c_{2}sin(t)+(tsin(t))/2-(tcos(t))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+y=sin(t)+cos(t)

y^{^{''}} + y = sin (t) + cos (t)

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

Solution steps

y^{''} (t) + y = sin (t) + cos (t)

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} - 6 y = 12 x - e^{x}

y^{^{''}} + 5 y^{^{'}} - 4 y = 8 t + 8

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{x}

d^{2} y = (2 x^{2} + 4) (x^{2} + 3 x)^{4}

What is the solution for y^{''}+y=sin(t)+cos(t) ?
The solution for y^{''}+y=sin(t)+cos(t) is y=c_{1}cos(t)+c_{2}sin(t)+(tsin(t))/2-(tcos(t))/2