Internal problem ID [4447]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {3 r-r^{\prime }+\theta ^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(3*r(theta)=diff(r(theta),theta)-theta^3,r(theta), singsol=all)
\[ r \left (\theta \right ) = -\frac {\theta ^{2}}{3}-\frac {\theta ^{3}}{3}-\frac {2 \theta }{9}-\frac {2}{27}+{\mathrm e}^{3 \theta } c_{1} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 30
DSolve[3*r[\[Theta]]==r'[\[Theta]]-\[Theta]^3,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to -\frac {1}{9} \theta (3 \theta (\theta +1)+2)+c_1 e^{3 \theta }-\frac {2}{27} \\ \end{align*}