Internal problem ID [13944]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.11 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+\cos \left (y\right )=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
Order:=5; dsolve(diff(y(x),x)+cos(y(x))=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )-\cos \left (y \left (0\right )\right ) x -\frac {\sin \left (2 y \left (0\right )\right ) x^{2}}{4}+\frac {\cos \left (y \left (0\right )\right ) \cos \left (2 y \left (0\right )\right ) x^{3}}{6}+\left (\frac {\sin \left (4 y \left (0\right )\right )}{32}+\frac {\sin \left (2 y \left (0\right )\right )}{24}\right ) x^{4}+O\left (x^{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 76
AsymptoticDSolveValue[y'[x]+Cos[y[x]]==0,y[x],{x,0,4}]
\[ y(x)\to \frac {1}{24} x^4 \left (5 \sin (c_1) \cos ^3(c_1)-\sin ^3(c_1) \cos (c_1)\right )+\frac {1}{6} x^3 \left (\cos ^3(c_1)-\sin ^2(c_1) \cos (c_1)\right )-\frac {1}{2} x^2 \sin (c_1) \cos (c_1)-x \cos (c_1)+c_1 \]