Internal problem ID [5381]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-2 x y-1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)=2*x*y(x)+1,y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {\sqrt {\pi }\, \operatorname {erf}\left (x \right )}{2}+c_{1} \right ) {\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 27
DSolve[y'[x]==2*x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{x^2} \left (\sqrt {\pi } \text {erf}(x)+2 c_1\right ) \\ \end{align*}