71.4.9 problem 9

Internal problem ID [14381]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 06:28:54 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x y}{1-y} \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 39

DSolve[D[y[x],x]==x*y[x]/(1-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ]\left [-\frac {x^2}{2}+c_1\right ] \\ y(x)\to 0 \\ \end{align*}