7.4.29 problem 29

Internal problem ID [101]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 29
Date solved : Friday, February 07, 2025 at 07:49:26 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+2 x y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(y(x),x)=1+2*x*y(x),y(x), singsol=all)
 

\[ y = \frac {\left (\sqrt {\pi }\, \operatorname {erf}\left (x \right )+2 c_1 \right ) {\mathrm e}^{x^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 27

DSolve[D[y[x],x]==1+2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{x^2} \left (\sqrt {\pi } \text {erf}(x)+2 c_1\right ) \]