Internal problem ID [1695]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 t -2 \,{\mathrm e}^{y t} \sin \left (2 t \right )+{\mathrm e}^{y t} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{y t} t \cos \left (2 t \right )\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.778 (sec). Leaf size: 36
dsolve([2*t-2*exp(t*y(t))*sin(2*t)+exp(t*y(t))*cos(2*t)*y(t)+(-3+exp(t*y(t))*t*cos(2*t))*diff(y(t),t) = 0,y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{3}-3 \LambertW \left (-\frac {t \cos \left (2 t \right ) {\mathrm e}^{\frac {t \left (t -1\right ) \left (t +1\right )}{3}}}{3}\right )-t}{3 t} \]
✓ Solution by Mathematica
Time used: 4.506 (sec). Leaf size: 41
DSolve[{2*t-2*Exp[t*y[t]]*Sin[2*t]+Exp[t*y[t]]*Cos[2*t]*y[t]+(-3+Exp[t*y[t]]*t*Cos[2*t])*y'[t] == 0,y[0]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} \left (-\frac {3 \text {ProductLog}\left (-\frac {1}{3} e^{\frac {1}{3} t \left (t^2-1\right )} t \cos (2 t)\right )}{t}+t^2-1\right ) \\ \end{align*}