Internal problem ID [5304]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }-2 s \,{\mathrm e}^{2 t}=-2 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 57
dsolve((2*s(t)-exp(2*t))*diff(s(t),t)=2*(s(t)*exp(2*t)-cos(2*t)),s(t), singsol=all)
\begin{align*} s \left (t \right ) = \frac {{\mathrm e}^{2 t}}{2}-\frac {\sqrt {{\mathrm e}^{4 t}-4 \sin \left (2 t \right )-4 c_{1}}}{2} s \left (t \right ) = \frac {{\mathrm e}^{2 t}}{2}+\frac {\sqrt {{\mathrm e}^{4 t}-4 \sin \left (2 t \right )-4 c_{1}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 15.59 (sec). Leaf size: 81
DSolve[(2*s[t]-Exp[2*t])*s'[t]==2*(s[t]*Exp[2*t]-Cos[2*t]),s[t],t,IncludeSingularSolutions -> True]
\begin{align*} s(t)\to \frac {1}{2} \left (e^{2 t}-i \sqrt {-e^{4 t}+4 \sin (2 t)-4 c_1}\right ) s(t)\to \frac {1}{2} \left (e^{2 t}+i \sqrt {-e^{4 t}+4 \sin (2 t)-4 c_1}\right ) \end{align*}