What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2 ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2 is y=c_{1}e^x+c_{2}xe^x+x^2+7x+13

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=1+3x+x^2

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

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

y^{^{''}} - 3 y^{^{'}} - 4 y = 5 cos (x) + 1389 e^{- 2 x}

x^{^{''}} - 18 x^{^{'}} + 81 x = 3 t e^{9 t}

y^{^{''}} + 2 y^{^{'}} + y = 2 x^{2} + 4 x + 2

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = e - x

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 5} e^{4 t}

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2 ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2 is y=c_{1}e^x+c_{2}xe^x+x^2+7x+13