15.1.20 problem 20

Internal problem ID [2860]
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 : 20
Date solved : Monday, January 27, 2025 at 06:20:28 AM
CAS classification : [_separable]

\begin{align*} y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.843 (sec). Leaf size: 55

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

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