Internal problem ID [5808]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
Order:=8; dsolve(diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-x^{2}+1\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{120} x^{5}-\frac {1}{1680} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[y''[x]-x*y'[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (1-x^2\right )+c_2 \left (-\frac {x^7}{1680}-\frac {x^5}{120}-\frac {x^3}{6}+x\right ) \]