36.2.8 problem 8

Internal problem ID [6301]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:55:28 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(diff(y(x),x)=y(x)/x+2*x+1,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (2 x +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 15

DSolve[D[y[x],x]==y[x]/x+2*x+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (2 x+\log (x)+c_1) \]