Solved by factoring the diﬀerential equation

Time used: 0.041 (sec)

\[\begin {aligned} x y y^{\prime }&=0 \end {aligned}\]

Writing the ode as

\begin{align*} \left (y\right )\left (y^{\prime }\right )&=0 \end{align*}

Therefore we need to solve the following equations

\begin{align*} y &= 0\tag {1} \\ y^{\prime } &= 0\tag {2} \end{align*}

Now each of the above equations is solved in turn.

Solving equation (1)

Entering zero order ode solverSolving for \(y\) from

\begin{align*} y = 0 \end{align*}

Solving gives

\begin{gather*} \begin {aligned} y &= 0\\ \end {aligned} \end{gather*}

Solving equation (2)

Entering ﬁrst order ode quadrature solverBecause the ODE has the form \(y^{\prime }=f(x)\), the solution requires only integration. Therefore

\begin{align*} dy &= \left (0\right ) \, dx\\ y &= \int { \left (0\right ) \, dx}\\ &= c_1 \end{align*}

Summary of solutions found

\begin{align*} y&=c_1\\ y&=0 \end{align*}