71.1.22 problem 36

Internal problem ID [14331]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 06:26:47 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}-9 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 69

dsolve(diff(y(x),x)^2-9*x*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= x^{3}+2 \sqrt {c_{1} x}\, x +c_{1} \\ y &= x^{3}-2 \sqrt {c_{1} x}\, x +c_{1} \\ y &= x^{3}-2 \sqrt {c_{1} x}\, x +c_{1} \\ y &= x^{3}+2 \sqrt {c_{1} x}\, x +c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 46

DSolve[(D[y[x],x])^2-9*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (-2 x^{3/2}+c_1\right ){}^2 \\ y(x)\to \frac {1}{4} \left (2 x^{3/2}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}