40.2.16 problem 41

Internal problem ID [6594]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 41
Date solved : Monday, January 27, 2025 at 02:14:51 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {2 x^{4}+4 c_1}}{2 x} \\ y &= \frac {\sqrt {2 x^{4}+4 c_1}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 46

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

\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ \end{align*}