29.7.2 problem 177

Internal problem ID [4777]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 177
Date solved : Monday, January 27, 2025 at 09:37:23 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {x}{-x^{2}+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 23

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

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