52.4.9 problem 17

Internal problem ID [8319]
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
Date solved : Monday, January 27, 2025 at 03:48:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 64

Order:=8; 
dsolve((1-2*sin(x))*diff(y(x),x$2)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{6} x^{3}-\frac {1}{6} x^{4}-\frac {1}{5} x^{5}-\frac {1}{4} x^{6}-\frac {85}{252} x^{7}\right ) y \left (0\right )+\left (x -\frac {1}{12} x^{4}-\frac {1}{10} x^{5}-\frac {2}{15} x^{6}-\frac {13}{72} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 77

AsymptoticDSolveValue[(1-2*Sin[x])*D[y[x],{x,2}]+x*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_2 \left (-\frac {13 x^7}{72}-\frac {2 x^6}{15}-\frac {x^5}{10}-\frac {x^4}{12}+x\right )+c_1 \left (-\frac {85 x^7}{252}-\frac {x^6}{4}-\frac {x^5}{5}-\frac {x^4}{6}-\frac {x^3}{6}+1\right ) \]