Internal problem ID [1384]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
II. Exercises 7.6. Page 374
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 y^{\prime } x^{3}+\left (3 x^{2}+1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
Order:=6; dsolve(2*x^2*(2+x^2)*diff(y(x),x$2)+7*x^3*diff(y(x),x)+(1+3*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \sqrt {x}\, \left (\left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1-\frac {3}{8} x^{2}+\frac {21}{128} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-\frac {1}{16} x^{2}+\frac {17}{512} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 77
AsymptoticDSolveValue[2*x^2*(2+x^2)*y''[x]+7*x^3*y'[x]+(1+3*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {21 x^4}{128}-\frac {3 x^2}{8}+1\right )+c_2 \left (\sqrt {x} \left (\frac {17 x^4}{512}-\frac {x^2}{16}\right )+\sqrt {x} \left (\frac {21 x^4}{128}-\frac {3 x^2}{8}+1\right ) \log (x)\right ) \]