What is the solution for (x^2+1)(dy)/(dx)+xy=3x,y(0)=4 ?

The solution for (x^2+1)(dy)/(dx)+xy=3x,y(0)=4 is y= 1/(sqrt(x^2+1))+3

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(x^2+1)(dy)/(dx)+xy=3x,y(0)=4

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

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

Solution steps

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

Solve separable ODE:

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

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

y \frac{d y}{d x} = 6 (y^{2} + 7)^{7}

\frac{1}{y} y^{^{'}} = b

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

\frac{( t ^{2} )}{x} d t = d x

\frac{d y}{d x} y = \frac{4 sin ( x )}{9 - 8 sin ( x )}

What is the solution for (x^2+1)(dy)/(dx)+xy=3x,y(0)=4 ?
The solution for (x^2+1)(dy)/(dx)+xy=3x,y(0)=4 is y= 1/(sqrt(x^2+1))+3