29.11.22 problem 313

Internal problem ID [4913]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 313
Date solved : Monday, January 27, 2025 at 09:50:25 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y \left (x \right ) = \frac {c_{1} x}{\left (x +1\right )^{3}} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 19

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

\begin{align*} y(x)\to \frac {c_1 x}{(x+1)^3} \\ y(x)\to 0 \\ \end{align*}