Internal problem ID [6159]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=8; dsolve((1+3*x^2)*diff(y(x),x$2)+13*x*diff(y(x),x)+7*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {7}{2} x^{2}+\frac {91}{8} x^{4}-\frac {1729}{48} x^{6}\right ) y \relax (0)+\left (x -\frac {10}{3} x^{3}+\frac {32}{3} x^{5}-\frac {704}{21} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 56
AsymptoticDSolveValue[(1+3*x^2)*y''[x]+13*x*y'[x]+7*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {704 x^7}{21}+\frac {32 x^5}{3}-\frac {10 x^3}{3}+x\right )+c_1 \left (-\frac {1729 x^6}{48}+\frac {91 x^4}{8}-\frac {7 x^2}{2}+1\right ) \]