What is the solution for (1+x^2)(dy)/(dx)-xy=0,y(2)=5 ?

The solution for (1+x^2)(dy)/(dx)-xy=0,y(2)=5 is y=(5sqrt(1+x^2)}{e^{\frac{ln(5))/2}}

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(1+x^2)(dy)/(dx)-xy=0,y(2)=5

(1 + x^{2}) \frac{d y}{d x} - x y = 0, y (2) = 5

y = \frac{5 1 + x ^{2}}{e ^{\frac{l n ( 5 )}{2}}}

Solution steps

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

Solve separable ODE:

y = \frac{5 1 + x ^{2}}{e ^{\frac{l n ( 5 )}{2}}}

y = \frac{5 1 + x ^{2}}{e ^{\frac{l n ( 5 )}{2}}}

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

3 \frac{d y}{d x} = \frac{4 x}{y ^{2}}

y^{^{'}} = 4 x + x y, y (0) = - 2

y^{^{'}} = 4 x + x y, y (0) = - 1

\frac{d y}{d x} y = 5 x^{3}

What is the solution for (1+x^2)(dy)/(dx)-xy=0,y(2)=5 ?
The solution for (1+x^2)(dy)/(dx)-xy=0,y(2)=5 is y=(5sqrt(1+x^2)}{e^{\frac{ln(5))/2}}