Internal problem ID [2425]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.4. page
758
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
Order:=6; dsolve(3*x^2*diff(y(x),x$2)+x*(1+3*x^2)*diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {2}{3}} \left (1+\frac {2}{5} x -\frac {3}{40} x^{2}-\frac {43}{660} x^{3}+\frac {31}{3696} x^{4}+\frac {2259}{261800} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+2 x +\frac {1}{2} x^{2}-\frac {5}{21} x^{3}-\frac {73}{840} x^{4}+\frac {827}{27300} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 83
AsymptoticDSolveValue[3*x^2*y''[x]+x*(1+3*x^2)*y'[x]-2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {827 x^5}{27300}-\frac {73 x^4}{840}-\frac {5 x^3}{21}+\frac {x^2}{2}+2 x+1\right )+c_1 x^{2/3} \left (\frac {2259 x^5}{261800}+\frac {31 x^4}{3696}-\frac {43 x^3}{660}-\frac {3 x^2}{40}+\frac {2 x}{5}+1\right ) \]