74.7.15 problem 15

Internal problem ID [16013]
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 : 15
Date solved : Thursday, March 13, 2025 at 07:13:39 AM
CAS classification : [_separable]

\begin{align*} \frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )}&=0 \end{align*}

✓ Maple. Time used: 1.323 (sec). Leaf size: 53

ode:=sin(2*t)/cos(2*y(t))+ln(y(t))/ln(t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ -\frac {i \pi \left (\operatorname {csgn}\left (t \right )-1\right ) \operatorname {csgn}\left (i t \right )}{8}+\frac {\pi \,\operatorname {csgn}\left (y\right )}{8}+\frac {\sin \left (2 y\right ) \ln \left (y\right )}{4}-\frac {\cos \left (2 t \right ) \ln \left (t \right )}{4}-\frac {\operatorname {Si}\left (2 y\right )}{4}+c_{1} +\frac {\operatorname {Ci}\left (2 t \right )}{4} = 0 \]

✓ Mathematica. Time used: 0.539 (sec). Leaf size: 44

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

\[ y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (2 K[1]) \log (K[1])dK[1]\&\right ]\left [\int _1^t-\log (K[2]) \sin (2 K[2])dK[2]+c_1\right ] \]

✓ Sympy. Time used: 145.488 (sec). Leaf size: 39

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

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