29.3.29 problem 83

Internal problem ID [4691]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 83
Date solved : Monday, January 27, 2025 at 09:31:50 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ y \left (x \right ) &= \frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.299 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to \frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to 0 \\ \end{align*}