Internal problem ID [1191]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x^{2}-2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 42
Order:=6; dsolve((1+3*x^2)*diff(y(x),x$2)+3*x^2*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+x^{2}-\frac {1}{3} x^{4}-\frac {3}{10} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{3} x^{3}-\frac {1}{4} x^{4}-\frac {4}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 52
AsymptoticDSolveValue[(1+3*x^2)*y''[x]+3*x^2*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {4 x^5}{15}-\frac {x^4}{4}+\frac {x^3}{3}+x\right )+c_1 \left (-\frac {3 x^5}{10}-\frac {x^4}{3}+x^2+1\right ) \]