74.7.59 problem 66

Internal problem ID [16057]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 66
Date solved : Thursday, March 13, 2025 at 07:38:06 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.892 (sec). Leaf size: 23

ode:=y(t)*sin(t/y(t))-(t+t*sin(t/y(t)))*diff(y(t),t) = 0; 
ic:=y(1) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} -\operatorname {Si}\left (t \,{\mathrm e}^{-\textit {\_Z}}\right )-\ln \left (2\right )+\operatorname {Si}\left (\frac {1}{2}\right )\right )} \]

✓ Mathematica. Time used: 0.173 (sec). Leaf size: 34

ode=y[t]*Sin[t/y[t]]-(t+t*Sin[t/y[t]])*D[y[t],t]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\log \left (\frac {y(t)}{t}\right )-\text {Si}\left (\frac {t}{y(t)}\right )=-\text {Si}\left (\frac {1}{2}\right )-\log (t)+\log (2),y(t)\right ] \]

✓ Sympy. Time used: 1.674 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(t*sin(t/y(t)) + t)*Derivative(y(t), t) + y(t)*sin(t/y(t)),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \log {\left (y{\left (t \right )} \right )} = \operatorname {Si}{\left (\frac {t}{y{\left (t \right )}} \right )} - \operatorname {Si}{\left (\frac {1}{2} \right )} + \log {\left (2 \right )} \]