Internal problem ID [14358]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )}=0} \]
✓ Solution by Maple
Time used: 0.687 (sec). Leaf size: 55
dsolve(( sin(2*t)/cos(2*y(t)) )+( ln(y(t))/ln(t) )*diff(y(t),t)=0,y(t), singsol=all)
\[ -\frac {i \pi \left (\operatorname {csgn}\left (t \right )-1\right ) \operatorname {csgn}\left (i t \right )}{8}+\frac {\pi \,\operatorname {csgn}\left (y \left (t \right )\right )}{8}+\frac {\sin \left (2 y \left (t \right )\right ) \ln \left (y \left (t \right )\right )}{4}-\frac {\cos \left (2 t \right ) \ln \left (t \right )}{4}-\frac {\operatorname {Si}\left (2 y \left (t \right )\right )}{4}+c_{1} +\frac {\operatorname {Ci}\left (2 t \right )}{4} = 0 \]
✓ Solution by Mathematica
Time used: 0.697 (sec). Leaf size: 50
DSolve[( Sin[2*t]/Cos[2*y[t]] )+( Log[y[t]]/Log[t] )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \text {InverseFunction}\left [\frac {1}{2} \log (\text {$\#$1}) \sin (2 \text {$\#$1})-\frac {\text {Si}(2 \text {$\#$1})}{2}\&\right ]\left [-\frac {\operatorname {CosIntegral}(2 t)}{2}+\frac {1}{2} \log (t) \cos (2 t)+c_1\right ] \]