Internal problem ID [5702]
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 4.4. REGULAR SINGULAR
POINTS. Page 175
Problem number: 4(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+\left (3-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: 0.047 (sec). Leaf size: 52
Order:=8; dsolve(2*x*diff(y(x),x$2)+(3-x)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} \left (1+\frac {1}{3} x +\frac {1}{15} x^{2}+\frac {1}{105} x^{3}+\frac {1}{945} x^{4}+\frac {1}{10395} x^{5}+\frac {1}{135135} x^{6}+\frac {1}{2027025} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \sqrt {x}+c_{1} \left (1+\frac {1}{2} x +\frac {1}{8} x^{2}+\frac {1}{48} x^{3}+\frac {1}{384} x^{4}+\frac {1}{3840} x^{5}+\frac {1}{46080} x^{6}+\frac {1}{645120} x^{7}+\mathrm {O}\left (x^{8}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 113
AsymptoticDSolveValue[2*x*y''[x]+(3-x)*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^7}{2027025}+\frac {x^6}{135135}+\frac {x^5}{10395}+\frac {x^4}{945}+\frac {x^3}{105}+\frac {x^2}{15}+\frac {x}{3}+1\right )+\frac {c_2 \left (\frac {x^7}{645120}+\frac {x^6}{46080}+\frac {x^5}{3840}+\frac {x^4}{384}+\frac {x^3}{48}+\frac {x^2}{8}+\frac {x}{2}+1\right )}{\sqrt {x}} \]