Internal problem ID [5865]
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. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 36(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=8; dsolve(x^2*diff(y(x),x$2)+(3*x-1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 53
AsymptoticDSolveValue[x^2*y''[x]+(3*x-1)*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (5040 x^7+720 x^6+120 x^5+24 x^4+6 x^3+2 x^2+x+1\right )+\frac {c_2 e^{-1/x}}{x} \]