What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=4x^2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-3(dy)/(dx)+2y=4x^2

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 x^{2}

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x^{2} + 6 x + 7

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x^{2} + 6 x + 7

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x^{2} + 6 x + 7

\int \frac{2 x ^{2}}{x ^{2} + 8} d x

\int 3 x^{3} - 2 x^{2} + 8 x - 6 d x

\int 2 a 1 + cos (θ) d θ

\frac{d}{d x} (cos (x) - \frac{1}{3} cos^{3} (x))

\int \frac{x - 5}{- 2 x + 2} d x

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