Internal problem ID [4477]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\theta r^{\prime }+3 r-\theta -1=0} \end {gather*}
✓ 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)
\[ r \left (\theta \right ) = \frac {\theta }{4}+\frac {1}{3}+\frac {c_{1}}{\theta ^{3}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 20
DSolve[\[Theta]*r'[\[Theta]]+(3*r[\[Theta]]-\[Theta]-1)==0,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to \frac {c_1}{\theta ^3}+\frac {\theta }{4}+\frac {1}{3} \\ \end{align*}