Internal problem ID [6172]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x \left (x +3\right ) y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 42
Order:=8; dsolve(2*x*(x+3)*diff(y(x),x$2)-3*(x+1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {3}{2}} \left (1+\frac {1}{15} x -\frac {1}{315} x^{2}+\frac {1}{2835} x^{3}-\frac {1}{18711} x^{4}+\frac {1}{104247} x^{5}-\frac {1}{521235} x^{6}+\frac {1}{2416635} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (1+\frac {2}{3} x +\frac {1}{9} x^{2}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 78
AsymptoticDSolveValue[2*x*(x+3)*y''[x]-3*(x+1)*y'[x]+2*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^2}{9}+\frac {2 x}{3}+1\right )+c_1 \left (\frac {x^7}{2416635}-\frac {x^6}{521235}+\frac {x^5}{104247}-\frac {x^4}{18711}+\frac {x^3}{2835}-\frac {x^2}{315}+\frac {x}{15}+1\right ) x^{3/2} \]