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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} + 2 x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} + 2 x

y = c_{1} + c_{2} e^{- x} + \frac{x ^{3}}{3} + 2 x

y^{^{''}} - 5 y^{^{'}} + 6 y = 5 x - 5

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y = t - 3 sin (2 t), y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''''}} - y = t e^{t} + sin (t)

y^{^{''}} + 81 y = 8 sin (9 t)

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