12.7.6 problem 6

Internal problem ID [1716]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:32:17 AM
CAS classification : [_linear]

\begin{align*} 5 y x +2 y+5+2 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve((5*x*y(x)+2*y(x)+5)+(2*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {5 x}{2}} c_1 -1}{x} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 21

DSolve[(5*x*y[x]+2*y[x]+5)+(2*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-1+c_1 e^{-5 x/2}}{x} \]