Internal problem ID [5485]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {x y y^{\prime \prime }-y^{\prime }-\left (y^{\prime }\right )^{3}=0} \end {gather*}
✗ Solution by Maple
dsolve(x*y(x)*diff(y(x),x$2)=diff(y(x),x)+(diff(y(x),x))^3,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 2.246 (sec). Leaf size: 103
DSolve[x*y''[x]==y'[x]+(y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-i e^{-c_1} \sqrt {-1+e^{2 c_1} x^2} \\ y(x)\to i e^{-c_1} \sqrt {-1+e^{2 c_1} x^2}+c_2 \\ y(x)\to c_2-i \sqrt {x^2} \\ y(x)\to i \sqrt {x^2}+c_2 \\ \end{align*}