Internal problem ID [6168]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 53
Order:=8; dsolve(2*x^2*(1-x)*diff(y(x),x$2)-x*(1+7*x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+3 x +6 x^{2}+10 x^{3}+15 x^{4}+21 x^{5}+28 x^{6}+36 x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} x \left (1+\frac {7}{3} x +\frac {21}{5} x^{2}+\frac {33}{5} x^{3}+\frac {143}{15} x^{4}+13 x^{5}+17 x^{6}+\frac {323}{15} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 96
AsymptoticDSolveValue[2*x^2*(1-x)*y''[x]-x*(1+7*x)*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x \left (\frac {323 x^7}{15}+17 x^6+13 x^5+\frac {143 x^4}{15}+\frac {33 x^3}{5}+\frac {21 x^2}{5}+\frac {7 x}{3}+1\right )+c_2 \sqrt {x} \left (36 x^7+28 x^6+21 x^5+15 x^4+10 x^3+6 x^2+3 x+1\right ) \]