37.2.6 problem 10.3.7

Internal problem ID [6403]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order. page 315
Problem number : 10.3.7
Date solved : Monday, January 27, 2025 at 02:00:39 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {\left (x^{2}+2 c_1 \right ) \left (x -1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 20

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

\[ y(x)\to \frac {1}{2} (x-1) \left (x^2+2 c_1\right ) \]