44.1.28 problem 30

Internal problem ID [6903]
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. Exercises 1.1 at page 12
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:34:32 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 29

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

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