30.5.14 problem 14

Internal problem ID [7513]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 04:41:08 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

ode:=diff(y(t),t) = (t*sec(y(t)/t)+y(t))/t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \arcsin \left (\ln \left (t \right )+c_1 \right ) t \]

✓ Mathematica. Time used: 0.239 (sec). Leaf size: 13

ode=D[y[t],t]==( t*Sec[ y[t]/t ]+y[t]  ) /t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t \arcsin (\log (t)+c_1) \end{align*}

✓ Sympy. Time used: 0.535 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (t*sec(y(t)/t) + y(t))/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = t \left (\operatorname {asin}{\left (C_{1} - \log {\left (t \right )} \right )} + \pi \right ), \ y{\left (t \right )} = - t \operatorname {asin}{\left (C_{1} - \log {\left (t \right )} \right )}\right ] \]