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}

y^{^{''}} + 8 y^{^{'}} + 20 y = 40, y (0) = 0, y^{^{'}} (0) = 0

\int csc (t) d t

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = x e^{x}

f (x) = 2 x^{3} - 8 x, (- 2, 0)

\int ((4 x + 3) \cdot (2 x^{2} + 3 x)^{3}) d x

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)}