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 : Sunday, March 30, 2025 at 10:51:44 AM
CAS classification : [_linear]

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

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

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

\[ r = \frac {\theta }{4}+\frac {1}{3}+\frac {c_1}{\theta ^{3}} \]

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

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

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

✓ Sympy. Time used: 0.198 (sec). Leaf size: 14

from sympy import * 
theta = symbols("theta") 
r = Function("r") 
ode = Eq(theta*Derivative(r(theta), theta) - theta + 3*r(theta) - 1,0) 
ics = {} 
dsolve(ode,func=r(theta),ics=ics)
 

\[ r{\left (\theta \right )} = \frac {C_{1}}{\theta ^{3}} + \frac {\theta }{4} + \frac {1}{3} \]