en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-2(dy)/(dx)+y=(x-1)e^x

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

(d^2y)/(dx^2)+(dy)/(dx)=sin(x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = sin (x)

y^{''}-81y=e^{9x}

y^{^{''}} - 81 y = e^{9 x}

x^{''}-4x^'+3x=2e^t-5e^{2t}

x^{^{''}} - 4 x^{^{'}} + 3 x = 2 e^{t} - 5 e^{2 t}

y^{''}+4y=t^2+7e^t,y(0)=0,y^'(0)=2

y^{^{''}} + 4 y = t^{2} + 7 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

y^{''}+y^'=(3t^2+2t)e^t+cos(t/2)

y^{^{''}} + y^{^{'}} = (3 t^{2} + 2 t) e^{t} + cos (\frac{t}{2})

Frequently Asked Questions (FAQ)

What is the solution for (d^2y)/(dx^2)-2*(dy)/(dx)+y=(x-1)*e^x ?
The solution for (d^2y)/(dx^2)-2*(dy)/(dx)+y=(x-1)*e^x is y=c_{1}e^x+c_{2}xe^x+(e^xx^3)/6-(e^xx^2)/2