What is the solution for ((dy))/((dx))= x/y ?

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

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((dy))/((dx))= x/y

\frac{( d y )}{( d x )} = \frac{x}{y}

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

Solution steps

\frac{( d y )}{( d x )} = \frac{x}{y}

Solve separable ODE:

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

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

\int_{1}^{2} (ln (x))^{2} d x

y = - x, x = - 1, x = 2, y = 0

y^{^{''}} + 8 y^{^{'}} + 65 y = 455, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{1}{x ^{2} + 6 x + 18} d x

x \to 1 lim (x - 4)

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