Internal problem ID [12323]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {x}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 85
dsolve(diff(y(x),x)=x/y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{2} y \left (x \right ) = -\frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{4} y \left (x \right ) = -\frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 79
DSolve[y'[x]==x/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [3]{-\frac {3}{2}} \sqrt [3]{x^2+2 c_1} y(x)\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} y(x)\to (-1)^{2/3} \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \end{align*}