Internal problem ID [919]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y x +y^{\prime }-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 14
dsolve([diff(y(x),x)+2*x*y(x)=x,y(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}+\frac {5 \,{\mathrm e}^{-x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 20
DSolve[{y'[x]+2*x*y[x]==x,y[0]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5 e^{-x^2}}{2}+\frac {1}{2} \\ \end{align*}