40.4.7 problem 19 (h)

Internal problem ID [6647]
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)
Date solved : Monday, January 27, 2025 at 02:16:43 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (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 &= \frac {{\mathrm e}^{2 t}}{2}-\frac {\sqrt {{\mathrm e}^{4 t}-4 \sin \left (2 t \right )-4 c_1}}{2} \\ s &= \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: 15.620 (sec). Leaf size: 81

DSolve[(2*s[t]-Exp[2*t])*D[s[t],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*}