Internal problem ID [871]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+2 y x -x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x) +2*x*y(x)= x,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}+{\mathrm e}^{-x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 26
DSolve[y'[x] +2*x*y[x]== x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2}+c_1 e^{-x^2} \\ y(x)\to \frac {1}{2} \\ \end{align*}