37.2.2 problem 10.3.3

Internal problem ID [6399]
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 : 10.3.3
Date solved : Monday, January 27, 2025 at 02:00:31 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 17

DSolve[{x^2*D[y[x],x]+2*x*y[x]-x+1==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(x-1)^2}{2 x^2} \]