Internal problem ID [6177]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots
Nonintegral. Exercises page 365
Problem number: 14.
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 }-5 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: 42
Order:=8; dsolve(2*x*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)-5*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+\frac {4}{3} x +\frac {4}{15} x^{2}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1+5 x +\frac {5}{2} x^{2}+\frac {1}{6} x^{3}-\frac {1}{168} x^{4}+\frac {1}{2520} x^{5}-\frac {1}{33264} x^{6}+\frac {1}{432432} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 76
AsymptoticDSolveValue[2*x*y''[x]+(1+2*x)*y'[x]-5*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {4 x^2}{15}+\frac {4 x}{3}+1\right )+c_2 \left (\frac {x^7}{432432}-\frac {x^6}{33264}+\frac {x^5}{2520}-\frac {x^4}{168}+\frac {x^3}{6}+\frac {5 x^2}{2}+5 x+1\right ) \]