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

The solution for (x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=2 is y= 1/((x^2+1)^{3/2)}+1

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} sec (t) = \frac{- y ^{17}}{16}

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

(x + 2) sin (y) + x cos (y) \frac{d y}{d x} = 0

\frac{d y}{d x} = - 600 y

f^{^{'}} (x) = 2 f (x)

What is the solution for (x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=2 ?
The solution for (x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=2 is y= 1/((x^2+1)^{3/2)}+1