Internal problem ID [4250]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 2. Separable equations. page
398
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y x -x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)-x*y(x)=x,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -1+2 \,{\mathrm e}^{\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 20
DSolve[{y'[x]-x*y[x]==x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{\frac {1}{2} \left (x^2-1\right )}-1 \\ \end{align*}