36.3.8 problem 8

Internal problem ID [6329]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:56:40 PM
CAS classification : [_linear]

\begin{align*} \theta r^{\prime }+3 r-\theta -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(theta*diff(r(theta),theta)+(3*r(theta)-theta-1)=0,r(theta), singsol=all)
 

\[ r = \frac {\theta }{4}+\frac {1}{3}+\frac {c_{1}}{\theta ^{3}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

DSolve[\[Theta]*D[ r[\[Theta]], \[Theta] ]+(3*r[\[Theta]]-\[Theta]-1)==0,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\[ r(\theta )\to \frac {c_1}{\theta ^3}+\frac {\theta }{4}+\frac {1}{3} \]