Internal problem ID [1708]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}+\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 43
dsolve(diff(y(t),t)=1/4*(1+cos(4*t))*y(t)-1/800*(1-cos(4*t))*y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{\frac {t}{4}+\frac {\sin \left (4 t \right )}{16}}}{c_{1}+\int -\frac {{\mathrm e}^{\frac {t}{4}+\frac {\sin \left (4 t \right )}{16}} \left (-1+\cos \left (4 t \right )\right )}{800}d t} \]
✓ Solution by Mathematica
Time used: 7.464 (sec). Leaf size: 122
DSolve[y'[t]==1/4*(1+Cos[4*t])*y[t]-1/800*(1-Cos[4*t])*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{\frac {1}{16} (4 t+\sin (4 t))}}{-\int _1^t-\frac {1}{400} e^{\frac {1}{16} (4 K[1]+\sin (4 K[1]))} \sin ^2(2 K[1])dK[1]+c_1} \\ y(t)\to 0 \\ y(t)\to -\frac {e^{\frac {1}{16} (4 t+\sin (4 t))}}{\int _1^t-\frac {1}{400} e^{\frac {1}{16} (4 K[1]+\sin (4 K[1]))} \sin ^2(2 K[1])dK[1]} \\ \end{align*}