What is the solution for y^{'''}+y^{''}=5x^2 ?

The solution for y^{'''}+y^{''}=5x^2 is y=c_{1}e^{-x}+c_{2}+c_{3}x+(5x^4}{12}-\frac{5x^3)/3+5x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{'''}+y^{''}=5x^2

y^{^{'''}} + y^{^{''}} = 5 x^{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} + 5 x^{2}

Solution steps

y^{'''} (x) + y^{''} (x) = 5 x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} + 5 x^{2}

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} + 5 x^{2}

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = (x + 1) e^{x}

y^{^{''}} - 4 y^{^{'}} + 2 y = 5 e^{x}

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

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 t} ln (t)

What is the solution for y^{'''}+y^{''}=5x^2 ?
The solution for y^{'''}+y^{''}=5x^2 is y=c_{1}e^{-x}+c_{2}+c_{3}x+(5x^4}{12}-\frac{5x^3)/3+5x^2