en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^3+3d^2+2d)y=x^2

Solution

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

Solution

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{3 x ^{2}}{4} + \frac{7 x}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{3 x ^{2}}{4} + \frac{7 x}{4}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{3 x ^{2}}{4} + \frac{7 x}{4}

Popular Examples

(d^2-2d+1)*y=x*e^x*cos(x)

(d^{2} - 2 d + 1) \cdot y = x \cdot e^{x} \cdot cos (x)

d^{2} (d^{2} + 1) y = 1

y^{'''}+3y^{''}=-36x^2+12x+42

y^{^{'''}} + 3 y^{^{''}} = - 36 x^{2} + 12 x + 42

y^{''}-y^'=e^{2x}*cos(e^x)

y^{^{''}} - y^{^{'}} = e^{2 x} \cdot cos (e^{x})

y^{''}+5y^'+4y=8x^2+3+2cos^2(x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + 3 + 2 cos^{2} (x)

Frequently Asked Questions (FAQ)

What is the solution for (d^3+3d^2+2d)y=x^2 ?
The solution for (d^3+3d^2+2d)y=x^2 is y=c_{1}+c_{2}e^{-x}+c_{3}e^{-2x}+(x^3)/6-(3x^2)/4+(7x)/4