40.5.1 problem 17

Internal problem ID [6666]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page 65
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:18:36 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)^2+x*y(x)*diff(y(x),x)-6*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= c_1 \,x^{2} \\ y &= \frac {c_1}{x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 26

DSolve[x^2*(D[y[x],x])^2+x*y[x]*D[y[x],x]-6*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x^3} \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}