Internal problem ID [5008]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 58
Order:=6; dsolve(sin(x)*diff(y(x),x$2)+cos(x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x \left (1-\frac {1}{2} x +\frac {1}{12} x^{2}+\frac {1}{48} x^{3}-\frac {3}{320} x^{4}+\frac {19}{9600} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (-x +\frac {1}{2} x^{2}-\frac {1}{12} x^{3}-\frac {1}{48} x^{4}+\frac {3}{320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (1-\frac {3}{4} x^{2}+\frac {1}{4} x^{3}-\frac {5}{576} x^{4}-\frac {437}{28800} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 85
AsymptoticDSolveValue[Sin[x]*y''[x]+Cos[x]*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{576} \left (7 x^4+192 x^3-720 x^2+576 x+576\right )-\frac {1}{48} x \left (x^3+4 x^2-24 x+48\right ) \log (x)\right )+c_2 \left (-\frac {3 x^5}{320}+\frac {x^4}{48}+\frac {x^3}{12}-\frac {x^2}{2}+x\right ) \]