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In Exercises $1-14,$ find the general solution of the differential equation.

$$

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

$$

The general solution of a differential equation is solving y as a function of x or..

\begin{equation}

y = f(x)

\end{equation}

Separate both variables using multiplication.

\begin{equation}

\frac{dy}{dx} * ydx = \frac{x}{y} * ydx \\

y*dy = x*dx

\end{equation}

Now integrate both sides in order to find the solution.

\begin{equation}

\int y\, dy = \int x\, dx \\

y^2 = x^2 + C

\end{equation}

Finally, Simplify and solve for y. Remember the constant \(\mathcal{C}\) is needed for indefinite integrals!

\begin{equation}

y = \sqrt{x^2 + C}

\end{equation}

Differential Equations

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Numerade Educator

Oregon State University

Baylor University

Idaho State University

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