Internal problem ID [4548]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2 y x -x +1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = \frac {\left (x -1\right )^{2}}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 17
DSolve[{x^2*y'[x]+2*x*y[x]-x+1==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x-1)^2}{2 x^2} \\ \end{align*}