44.6.43 problem 43

Internal problem ID [7187]
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 : 43
Date solved : Tuesday, February 04, 2025 at 12:45:44 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 37

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

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