Internal problem ID [4773]
Book: Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section: Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page
300
Problem number: 7.3.101 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }+\left (x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^3*diff(y(x),x$2)+(1+x)*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 222
AsymptoticDSolveValue[x^3*y''[x]+(1+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 e^{-\frac {2 i}{\sqrt {x}}} x^{3/4} \left (\frac {520667425699057 i x^{9/2}}{131941395333120}-\frac {21896102683 i x^{7/2}}{21474836480}+\frac {19100991 i x^{5/2}}{41943040}-\frac {3367 i x^{3/2}}{8192}-\frac {194208949785748261 x^5}{21110623253299200}+\frac {5189376335871 x^4}{2748779069440}-\frac {846810601 x^3}{1342177280}+\frac {205387 x^2}{524288}-\frac {273 x}{512}+\frac {13 i \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {x}}} x^{3/4} \left (-\frac {520667425699057 i x^{9/2}}{131941395333120}+\frac {21896102683 i x^{7/2}}{21474836480}-\frac {19100991 i x^{5/2}}{41943040}+\frac {3367 i x^{3/2}}{8192}-\frac {194208949785748261 x^5}{21110623253299200}+\frac {5189376335871 x^4}{2748779069440}-\frac {846810601 x^3}{1342177280}+\frac {205387 x^2}{524288}-\frac {273 x}{512}-\frac {13 i \sqrt {x}}{16}+1\right ) \]