Internal problem ID [5898]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. CHAPTER 6 IN REVIEW.
Page 271
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1-2 \sin \relax (x )\right ) y^{\prime \prime }+x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 59
Order:=8; dsolve((1-2*sin(x))*diff(y(x),x$2)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{3}-\frac {1}{6} x^{4}-\frac {1}{5} x^{5}-\frac {1}{4} x^{6}-\frac {85}{252} x^{7}\right ) y \relax (0)+\left (x -\frac {1}{12} x^{4}-\frac {1}{10} x^{5}-\frac {2}{15} x^{6}-\frac {13}{72} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 77
AsymptoticDSolveValue[(1-2*Sin[x])*y''[x]+x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {13 x^7}{72}-\frac {2 x^6}{15}-\frac {x^5}{10}-\frac {x^4}{12}+x\right )+c_1 \left (-\frac {85 x^7}{252}-\frac {x^6}{4}-\frac {x^5}{5}-\frac {x^4}{6}-\frac {x^3}{6}+1\right ) \]