40.2.22 problem 47

Internal problem ID [6600]
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 : 47
Date solved : Monday, January 27, 2025 at 02:15:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 18

dsolve([(x^2+y(x)^2)+x*y(x)*diff(y(x),x)= 0,y(1) = -1],y(x), singsol=all)
 

\[ y = -\frac {\sqrt {-2 x^{4}+6}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 26

DSolve[{(x^2+y[x]^2)+x*y[x]*D[y[x],x]==0,{y[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {3-x^4}}{\sqrt {2} x} \]