Internal problem ID [1698]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y-y^{2} \cos \left (t \right )=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 129
dsolve(diff(y(t),t)= 1+y(t)+y(t)^2*cos(t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\operatorname {csgn}\left (\sin \left (\frac {t}{2}\right )\right ) \left (\left (-4 \cos \left (t \right )-\operatorname {csgn}\left (\sin \left (\frac {t}{2}\right )\right )+1\right ) \operatorname {MathieuC}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )-4 c_{1} \left (\cos \left (t \right )+\frac {\operatorname {csgn}\left (\sin \left (\frac {t}{2}\right )\right )}{4}-\frac {1}{4}\right ) \operatorname {MathieuS}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )+\left (-1+\operatorname {csgn}\left (\sin \left (\frac {t}{2}\right )\right )\right ) \left (c_{1} \operatorname {MathieuSPrime}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )+\operatorname {MathieuCPrime}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )\right )\right )}{2 \left (-c_{1} \operatorname {MathieuS}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )+c_{1} \operatorname {MathieuSPrime}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )-\operatorname {MathieuC}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )+\operatorname {MathieuCPrime}\left (-1, -2, \arccos \left (\cos \left (\frac {t}{2}\right )\right )\right )\right ) \cos \left (t \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[t]== 1+y[t]+y[t]^2*Cos[t],y[t],t,IncludeSingularSolutions -> True]
Not solved