Internal problem ID [6256]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 40
Order:=8; dsolve(2*x*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+\frac {2}{3} x +\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1+3 x +\frac {1}{2} x^{2}-\frac {1}{30} x^{3}+\frac {1}{280} x^{4}-\frac {1}{2520} x^{5}+\frac {1}{23760} x^{6}-\frac {1}{240240} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 69
AsymptoticDSolveValue[2*x*y''[x]+(1+2*x)*y'[x]-3*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {x^7}{240240}+\frac {x^6}{23760}-\frac {x^5}{2520}+\frac {x^4}{280}-\frac {x^3}{30}+\frac {x^2}{2}+3 x+1\right )+c_1 \left (\frac {2 x}{3}+1\right ) \sqrt {x} \]