Internal problem ID [5056]
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]
\[ \boxed {x^{2} y^{\prime }+2 x y=x -1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\left (x -1\right )^{2}}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 17
DSolve[{x^2*y'[x]+2*x*y[x]-x+1==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(x-1)^2}{2 x^2} \]