What is the solution for (dy)/(dx)=sin^2(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=sin^2(x)

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

y = \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = sin^{2} (x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int sin^{2} (x) d x = \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + c_{1}

y = \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + c_{1}

\int_{1}^{2} \frac{x}{( x + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{3}{( x + 2 ) ^{2}})

y^{^{'}} = e^{4 x} - 3 x

\frac{d}{d x} (2 cot (\frac{x}{2}))

y^{^{'}} = x^{2} - y

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