50.7.2 problem 1(b)

Internal problem ID [7906]
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)
Date solved : Monday, January 27, 2025 at 03:31:47 PM
CAS classification : [NONE]

\begin{align*} x y y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \end{align*}

✗ 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: 1.783 (sec). Leaf size: 103

DSolve[x*D[y[x],{x,2}]==D[y[x],x]+(D[y[x],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*}