15.4.9 problem 10

Internal problem ID [2922]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 10
Date solved : Monday, January 27, 2025 at 06:56:06 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

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

\[ y = \left (x^{2}+c_1 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 17

DSolve[(y[x]*Exp[x]-2*x)+Exp[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (x^2+c_1\right ) \]