What is the solution for (x^2+1)(dy)/(dx)+3xy=3x ?

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

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(x^2+1)(dy)/(dx)+3xy=3x

(x^{2} + 1) \frac{d y}{d x} + 3 x y = 3 x

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

Solution steps

(x^{2} + 1) \frac{d y}{d x} + 3 x y = 3 x

Solve separable ODE:

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

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

\frac{d y}{d x} y = 2 x^{2} - 13 x + 6

\frac{d y}{d x} = \frac{( x + x y ^{2} )}{4 y}

\frac{d y}{d x} = \frac{6 x ^{2} + 4}{8 y ^{3} + 1}, y (0) = 1

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

y^{^{'}} - 6 y = 12, y (0) = 0

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