Internal problem ID [4955]
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`]]
\[ \boxed {3 r-r^{\prime }=-\theta ^{3}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.052 (sec). Leaf size: 33
DSolve[3*r[\[Theta]]==r'[\[Theta]]-\[Theta]^3,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\[ r(\theta )\to \frac {1}{27} \left (-9 \theta ^3-9 \theta ^2-6 \theta -2\right )+c_1 e^{3 \theta } \]