Internal problem ID [2423]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (6 x +1\right ) y=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: 47
Order:=6; dsolve(3*x^2*diff(y(x),x$2)+x*(7+3*x)*diff(y(x),x)+(1+6*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1-3 x +\frac {9}{4} x^{2}-\frac {27}{28} x^{3}+\frac {81}{280} x^{4}-\frac {243}{3640} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) x^{\frac {1}{3}}+c_{2} \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) x}{x^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 84
AsymptoticDSolveValue[3*x^2*y''[x]+x*(7+3*x)*y'[x]+(1+6*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right )}{\sqrt [3]{x}}+\frac {c_2 \left (-\frac {243 x^5}{3640}+\frac {81 x^4}{280}-\frac {27 x^3}{28}+\frac {9 x^2}{4}-3 x+1\right )}{x} \]