Internal problem ID [6135]
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]
\[ \boxed {-2 x y+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)=2*x*y(x)+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\sqrt {\pi }\, \operatorname {erf}\left (x \right )+2 c_{1} \right ) {\mathrm e}^{x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 27
DSolve[y'[x]==2*x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{x^2} \left (\sqrt {\pi } \text {erf}(x)+2 c_1\right ) \]