44.3.20 problem 28

Internal problem ID [7001]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:40:32 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x)-2*x*y(x)=exp(x),y(x), singsol=all)
 

\[ y = \frac {\left (\sqrt {\pi }\, {\mathrm e}^{\frac {1}{4}} \operatorname {erf}\left (-\frac {1}{2}+x \right )+2 c_{1} \right ) {\mathrm e}^{x^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.104 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{2} e^{x^2} \left (-\sqrt [4]{e} \sqrt {\pi } \text {erf}\left (\frac {1}{2}-x\right )+2 c_1\right ) \]