29.8.34 problem 239

Internal problem ID [4839]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 239
Date solved : Monday, January 27, 2025 at 09:42:11 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 72

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

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