37.2.5 problem 10.3.6

Internal problem ID [6402]
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 : 10.3.6
Date solved : Monday, January 27, 2025 at 02:00:37 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 27

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

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