12.2.33 problem 33

Internal problem ID [1569]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 33
Date solved : Monday, January 27, 2025 at 05:00:31 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve([diff(y(x),x)+2*x*y(x)=x,y(0) = 3],y(x), singsol=all)
 

\[ y = \frac {1}{2}+\frac {5 \,{\mathrm e}^{-x^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 20

DSolve[{D[y[x],x]+2*x*y[x]==x,y[0]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 e^{-x^2}}{2}+\frac {1}{2} \]