44.6.44 problem 44

Internal problem ID [7188]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 44
Date solved : Tuesday, February 04, 2025 at 12:45:49 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\sqrt {\pi }}{2} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 17

dsolve([diff(y(x),x)-2*x*y(x)=-1,y(0) = 1/2*Pi^(1/2)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 23

DSolve[{D[y[x],x]-2*x*y[x]==-1,{y[0]==Sqrt[Pi]/2}},y[x],x,IncludeSingularSolutions -> True]
 

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