Internal problem ID [1415]
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
III. Exercises 7.7. Page 389
Problem number: Example 7.7.3 page 385.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 35
Order:=6; dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(3+10*x^2)*diff(y(x),x)-(15-14*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1-\frac {5}{2} x^{2}+\frac {35}{8} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-203212800+101606400 x^{2}-25401600 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{5}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 46
AsymptoticDSolveValue[x^2*(1+x^2)*y''[x]+x*(3+10*x^2)*y'[x]-(15-14*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^5}-\frac {1}{2 x^3}+\frac {1}{8 x}\right )+c_2 \left (\frac {35 x^7}{8}-\frac {5 x^5}{2}+x^3\right ) \]