Internal problem ID [5849]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {3 x y^{\prime \prime }+\left (2-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(3*x*diff(y(x),x$2)+(2-x)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} \left (1+\frac {1}{3} x +\frac {1}{18} x^{2}+\frac {1}{162} x^{3}+\frac {1}{1944} x^{4}+\frac {1}{29160} x^{5}+\frac {1}{524880} x^{6}+\frac {1}{11022480} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1+\frac {1}{2} x +\frac {1}{10} x^{2}+\frac {1}{80} x^{3}+\frac {1}{880} x^{4}+\frac {1}{12320} x^{5}+\frac {1}{209440} x^{6}+\frac {1}{4188800} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 113
AsymptoticDSolveValue[3*x*y''[x]+(2-x)*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {x^7}{11022480}+\frac {x^6}{524880}+\frac {x^5}{29160}+\frac {x^4}{1944}+\frac {x^3}{162}+\frac {x^2}{18}+\frac {x}{3}+1\right )+c_2 \left (\frac {x^7}{4188800}+\frac {x^6}{209440}+\frac {x^5}{12320}+\frac {x^4}{880}+\frac {x^3}{80}+\frac {x^2}{10}+\frac {x}{2}+1\right ) \]