What is the solution for (d^2y)/(dx^2)-y=sin^2(x) ?

The solution for (d^2y)/(dx^2)-y=sin^2(x) is y=c_{1}e^x+c_{2}e^{-x}-sin^2(x)-2/5 cos(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-y=sin^2(x)

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

y = c_{1} e^{x} + c_{2} e^{- x} - sin^{2} (x) - \frac{2}{5} cos (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - sin^{2} (x) - \frac{2}{5} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- x} - sin^{2} (x) - \frac{2}{5} cos (2 x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e x cos (5 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = \frac{12 e ^{4 x}}{1 + e ^{2 x}}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x} ln ( x )}{x}

y^{^{''}} + 2 y^{^{'}} + 5 y = 8 e^{- t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x, y (0) = - 5, y^{^{'}} (0) = 1

What is the solution for (d^2y)/(dx^2)-y=sin^2(x) ?
The solution for (d^2y)/(dx^2)-y=sin^2(x) is y=c_{1}e^x+c_{2}e^{-x}-sin^2(x)-2/5 cos(2x)