Internal problem ID [4381]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }-y-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 9
dsolve([x*diff(y(x),x)-y(x)=x^2,y(2) = 6],y(x), singsol=all)
\[ y \relax (x ) = \left (x +1\right ) x \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 10
DSolve[{x*y'[x]-y[x]==x^2,{y[2]==6}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (x+1) \\ \end{align*}