What is the solution for y^{'''}-3y^{''}=sin(x) ?

The solution for y^{'''}-3y^{''}=sin(x) is y=c_{1}e^{3x}+c_{2}+c_{3}x+3/10 sin(x)+1/10 cos(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{'''}-3y^{''}=sin(x)

y^{^{'''}} - 3 y^{^{''}} = sin (x)

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

Solution steps

y^{'''} (x) - 3 y^{''} (x) = sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

y = c_{1} e^{3 x} + c_{2} + c_{3} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

2 y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{x}}{cos ( x )}

y^{^{''}} - 10 y^{^{'}} + 26 y = 4

y^{^{''}} - 13 y^{^{'}} + 40 y = 27 + 40 x

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + 1 = 0

(d^{2} + d - 6) y = e^{- 3 x}

What is the solution for y^{'''}-3y^{''}=sin(x) ?
The solution for y^{'''}-3y^{''}=sin(x) is y=c_{1}e^{3x}+c_{2}+c_{3}x+3/10 sin(x)+1/10 cos(x)