Internal problem ID [963]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear
Equations. Section 2.3 Page 60
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(diff(y(x),x)=2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 18
DSolve[y'[x]==2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x^2} \\ y(x)\to 0 \\ \end{align*}