Internal problem ID [13068]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{x}-\frac {x^{2}}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
dsolve(diff(y(x),x)=y(x)/x+(x/y(x))^2,y(x), singsol=all)
\begin{align*} y = \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}} x y = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x y = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 63
DSolve[y'[x]==y[x]/x+(x/y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \end{align*}