Internal problem ID [6169]
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: 6.
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 }+5 \left (1-2 x \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: 0.024 (sec). Leaf size: 40
Order:=8; dsolve(2*x*diff(y(x),x$2)+5*(1-2*x)*diff(y(x),x)-5*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} \left (1+x +\frac {15}{14} x^{2}+\frac {125}{126} x^{3}+\frac {625}{792} x^{4}+\frac {625}{1144} x^{5}+\frac {625}{1872} x^{6}+\frac {3125}{17136} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) x^{\frac {3}{2}}+c_{1} \left (1+10 x +\mathrm {O}\left (x^{8}\right )\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 65
AsymptoticDSolveValue[2*x*y''[x]+5*(1-2*x)*y'[x]-5*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to \frac {c_2 (10 x+1)}{x^{3/2}}+c_1 \left (\frac {3125 x^7}{17136}+\frac {625 x^6}{1872}+\frac {625 x^5}{1144}+\frac {625 x^4}{792}+\frac {125 x^3}{126}+\frac {15 x^2}{14}+x+1\right ) \]