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

The solution for (dy)/(dx)+2/x y= 3/x is y=(c_{1})/(2x^2)+3/2

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(dy)/(dx)+2/x y= 3/x

\frac{d y}{d x} + \frac{2}{x} y = \frac{3}{x}

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

Solution steps

\frac{d y}{d x} + \frac{2}{x} y = \frac{3}{x}

Solve separable ODE:

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

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

y^{^{'}} x + 3 y = 3

\frac{( t ^{2} - 16 t + 48 ) d y}{d t} = y

\frac{d y}{d t} - 2 t \cdot y = t

\frac{d y}{d t} = 2 y t, y (1) = 7

e^{- y} d x + (1 + x^{2}) d y = 0

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