What is the solution for (x^2+1)y^'+9x(y-1)=0,y(0)=2 ?

The solution for (x^2+1)y^'+9x(y-1)=0,y(0)=2 is y= 1/((x^2+1)^{9/2)}+1

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(x^2+1)y^'+9x(y-1)=0,y(0)=2

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 2

y = \frac{1}{( x ^{2} + 1 ) ^{\frac{9}{2}}} + 1

Solution steps

(x^{2} + 1) y^{'} (x) + 9 x (y - 1) = 0

Solve separable ODE:

y = \frac{1}{( x ^{2} + 1 ) ^{\frac{9}{2}}} + 1

y = \frac{1}{( x ^{2} + 1 ) ^{\frac{9}{2}}} + 1

\frac{d P}{d t} - a P = b

d x + e^{9 x} d y = 0

\frac{d}{d x} (- 2 x - 3 x^{3})

cos (\frac{1}{4} t)

\int (1 + 3 x) d x

What is the solution for (x^2+1)y^'+9x(y-1)=0,y(0)=2 ?
The solution for (x^2+1)y^'+9x(y-1)=0,y(0)=2 is y= 1/((x^2+1)^{9/2)}+1