Internal problem ID [6562]
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. Section 6.2
SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+x^{2} y^{\prime }+x y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
Order:=8; dsolve(diff(y(x),x$2)+x^2*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{6} x^{3}+\frac {1}{45} x^{6}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{4}+\frac {5}{252} x^{7}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[x]+x^2*y'[x]+x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {5 x^7}{252}-\frac {x^4}{6}+x\right )+c_1 \left (\frac {x^6}{45}-\frac {x^3}{6}+1\right ) \]