36.2.6 problem 6

Internal problem ID [6299]
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
Date solved : Monday, January 27, 2025 at 01:55:25 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(3*r(theta)=diff(r(theta),theta)-theta^3,r(theta), singsol=all)
 

\[ r = -\frac {\theta ^{2}}{3}-\frac {\theta ^{3}}{3}-\frac {2 \theta }{9}-\frac {2}{27}+{\mathrm e}^{3 \theta } c_{1} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 33

DSolve[3*r[\[Theta]]==D[ r[\[Theta]], \[Theta] ]-\[Theta]^3,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\[ r(\theta )\to \frac {1}{27} \left (-9 \theta ^3-9 \theta ^2-6 \theta -2\right )+c_1 e^{3 \theta } \]