What is the solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=3e^{7x} ?

The solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=3e^{7x} is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3e^{7x}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-14(dy)/(dx)+49y=3e^{7x}

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 3 e^{7 x}

Solve linear ODE:

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

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

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 6 y = t + e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = 68 cos (3 x)

x^{^{''}} - 9 x - 1 = 0

y^{^{''}} - y^{^{'}} = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = cos (7 t)

What is the solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=3e^{7x} ?
The solution for (d^2y)/(dx^2)-14(dy)/(dx)+49y=3e^{7x} is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3e^{7x}x^2)/2