What is the solution for (x^2-2)(dy)/(dx)-xy=0 ?

The solution for (x^2-2)(dy)/(dx)-xy=0 is y=c_{1}sqrt(x^2-2)

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(x^2-2)(dy)/(dx)-xy=0

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

y = c_{1} x^{2} - 2

Solution steps

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

Solve separable ODE:

y = c_{1} x^{2} - 2

y = c_{1} x^{2} - 2

4 y d x + x d y = 0

2 x y^{^{'}} = 4 - y^{2}

y (1 + cos (x) y) d x + x (1 + cos (x) y) d y = 0

t \frac{d y}{d t} = 16 y

2 x e^{2 t} d t + (1 + e^{2 t}) d x = 0

What is the solution for (x^2-2)(dy)/(dx)-xy=0 ?
The solution for (x^2-2)(dy)/(dx)-xy=0 is y=c_{1}sqrt(x^2-2)