Internal problem ID [5718]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.6. Gauss’s Hypergeometric
Equation. Page 187
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 52
Order:=8; dsolve((2*x^2+2*x)*diff(y(x),x$2)+(1+5*x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-x^{7}+x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (\sqrt {x}\, c_{1}+c_{2}\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 73
AsymptoticDSolveValue[(2*x^2+2*x)*y''[x]+(1+5*x)*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \sqrt {x} \left (-x^7+x^6-x^5+x^4-x^3+x^2-x+1\right )+c_2 \left (-x^7+x^6-x^5+x^4-x^3+x^2-x+1\right ) \]