Internal problem ID [13651]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.9 b(iii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
Order:=7; dsolve(diff(y(x),x$2)+sin(x)*diff(y(x),x)+cos(x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{6} x^{4}-\frac {31}{720} x^{6}\right ) y \left (0\right )+\left (x -\frac {1}{3} x^{3}+\frac {1}{10} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{7}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]+Sin[x]*y'[x]+Cos[x]*y[x]==0,y[x],{x,0,6}]
\[ y(x)\to c_2 \left (\frac {x^5}{10}-\frac {x^3}{3}+x\right )+c_1 \left (-\frac {31 x^6}{720}+\frac {x^4}{6}-\frac {x^2}{2}+1\right ) \]