15.8.28 problem 29

Internal problem ID [3031]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 29
Date solved : Monday, January 27, 2025 at 07:09:33 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y \left (1+y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.474 (sec). Leaf size: 76

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

\begin{align*} y(x)\to -\frac {i e^{c_1}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to \frac {i e^{c_1}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}