Internal problem ID [6266]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. Miscellaneous Exercises. page 394
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-x \left (1+2 x \right ) y^{\prime }+\left (3 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 41
Order:=8; dsolve(2*x^2*diff(y(x),x$2)-x*(1+2*x)*diff(y(x),x)+(1+3*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1-2 x +\mathrm {O}\left (x^{8}\right )\right )+c_{2} x \left (1-\frac {1}{3} x -\frac {1}{30} x^{2}-\frac {1}{210} x^{3}-\frac {1}{1512} x^{4}-\frac {1}{11880} x^{5}-\frac {1}{102960} x^{6}-\frac {1}{982800} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 70
AsymptoticDSolveValue[2*x^2*y''[x]-x*(1+2*x)*y'[x]+(1+3*x)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x \left (-\frac {x^7}{982800}-\frac {x^6}{102960}-\frac {x^5}{11880}-\frac {x^4}{1512}-\frac {x^3}{210}-\frac {x^2}{30}-\frac {x}{3}+1\right )+c_2 (1-2 x) \sqrt {x} \]