8.4.15 problem 15

Internal problem ID [718]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 15
Date solved : Wednesday, February 05, 2025 at 03:51:28 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 20

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

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