What is the solution for y^'=((2y+3))/(x^2) ?

The solution for y^'=((2y+3))/(x^2) is y=(e^{(-2+2c_{1}x)/x})/(2)-3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=((2y+3))/(x^2)

y^{^{'}} = \frac{( 2 y + 3 )}{x ^{2}}

y = \frac{e ^{\frac{- 2 + 2 c _{1} x}{x}}}{2} - \frac{3}{2}

Solution steps

y^{'} (x) = \frac{( 2 y + 3 )}{x ^{2}}

Solve separable ODE:

y = \frac{e ^{\frac{- 2 + 2 c _{1} x}{x}}}{2} - \frac{3}{2}

y = \frac{e ^{\frac{- 2 + 2 c _{1} x}{x}}}{2} - \frac{3}{2}

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

d x - \frac{d y}{1 + y ^{2}} = 0

\frac{d y}{d x} = \frac{2 x y}{x ^{2} + 1}, y (1) = 2

x d x - y d y = x y (x d y - y d x)

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

What is the solution for y^'=((2y+3))/(x^2) ?
The solution for y^'=((2y+3))/(x^2) is y=(e^{(-2+2c_{1}x)/x})/(2)-3/2