Internal problem ID [1216]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(1+2*x^2)*diff(y(x),x$2)-9*x*diff(y(x),x)-6*y(x)=0,y(0) = 1, D(y)(0) = -1],y(x),type='series',x=0);
\[ y \relax (x ) = 1-x +3 x^{2}-\frac {5}{2} x^{3}+5 x^{4}-\frac {21}{8} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[{(1+2*x^2)*y''[x]-9*x*y'[x]-6*y[x]==0,{y[0]==1,y'[0]==-1}},y[x],{x,0,5}]
\[ y(x)\to -\frac {21 x^5}{8}+5 x^4-\frac {5 x^3}{2}+3 x^2-x+1 \]