Internal problem ID [68]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 15.
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) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([2*x*y(x)+diff(y(x),x) = x,y(0) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}-\frac {5 \,{\mathrm e}^{-x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 20
DSolve[{2*x*y[x]+y'[x] == x,y[0]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2}-\frac {5 e^{-x^2}}{2} \\ \end{align*}