Internal problem ID [1200]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page
318
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+\left (1+2 x \right ) x y^{\prime }-\left (6 x +4\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)+x*(1+2*x)*diff(y(x),x)-(4+6*x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{2} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (\ln \left (x \right ) \left (576 x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\left (-144+192 x -288 x^{2}+576 x^{3}-576 x^{4}-576 x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 48
AsymptoticDSolveValue[x^2*(1+x)*y''[x]+x*(1+2*x)*y'[x]-(4+6*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x^2+c_1 \left (\frac {3 x^4-12 x^3+6 x^2-4 x+3}{3 x^2}-4 x^2 \log (x)\right ) \]