74.7.15 problem 15

Internal problem ID [16092]
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 : Tuesday, January 28, 2025 at 08:39:28 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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