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

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

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

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

y = c_{1} x^{2} - 3 + 1

Solution steps

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

Solve separable ODE:

y = c_{1} x^{2} - 3 + 1

y = c_{1} x^{2} - 3 + 1

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

x^{2} y \frac{d y}{d x} + 2 x y^{2} = 0

\frac{d y}{d x} = \frac{x sin ( x )}{y}, y (0) = - 1

\frac{d y}{d x} = a y

\frac{d y}{d x} = x \cdot y

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