15.1.2 problem 2

Internal problem ID [2842]
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 : 2
Date solved : Monday, January 27, 2025 at 06:19:33 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}-c_1 -1} \\ y &= -\sqrt {c_1 \,x^{2}-c_1 -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.270 (sec). Leaf size: 61

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

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