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

The solution for y^{''}+9y=2x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+(2x^2)/9-4/81

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+9y=2x^2

y^{^{''}} + 9 y = 2 x^{2}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{2 x ^{2}}{9} - \frac{4}{81}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{2 x ^{2}}{9} - \frac{4}{81}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{2 x ^{2}}{9} - \frac{4}{81}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 8 y = cos (x)

2 \frac{d ^{2} y}{d x ^{2}} + 1 \frac{d y}{d x} + 1 y = 2

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} + 6 y = 2 t

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{- 2 x} - e^{x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 1 - 2 x^{2}

What is the solution for y^{''}+9y=2x^2 ?
The solution for y^{''}+9y=2x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+(2x^2)/9-4/81