What is the solution for y^{''}-2y^'+17y=289x^2+9 ?

The solution for y^{''}-2y^'+17y=289x^2+9 is y=e^x(c_{1}cos(4x)+c_{2}sin(4x))+17x^2+4x-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'+17y=289x^2+9

y^{^{''}} - 2 y^{^{'}} + 17 y = 289 x^{2} + 9

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

Solution steps

y^{''} (x) - 2 y^{'} (x) + 17 y = 289 x^{2} + 9

Solve linear ODE:

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

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

- x^{^{''}} - 4 x = t^{2}

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

x^{^{''}} + 3 x^{^{'}} + 33 x = 9 cos (5 t)

y^{^{''}} + 4 y^{^{'}} + 3 y - 3 x = 0

What is the solution for y^{''}-2y^'+17y=289x^2+9 ?
The solution for y^{''}-2y^'+17y=289x^2+9 is y=e^x(c_{1}cos(4x)+c_{2}sin(4x))+17x^2+4x-1