15.1.6 problem 6

Internal problem ID [2846]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 6
Date solved : Monday, January 27, 2025 at 06:19:44 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

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

\begin{align*} y &= \frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_1 \right )}}{x^{2}-1} \\ y &= -\frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_1 \right )}}{x^{2}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.389 (sec). Leaf size: 133

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

\begin{align*} y(x)\to -\frac {\sqrt {-x^2+1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {-x^2+1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to -\frac {\sqrt {1-x^2}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {1-x^2}}{\sqrt {x^2-1}} \\ \end{align*}