Internal problem ID [6164]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 x \left (1+x \right ) y^{\prime \prime }+3 \left (1+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: 0.062 (sec). Leaf size: 40
Order:=8; dsolve(2*x*(x+1)*diff(y(x),x$2)+3*(x+1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} \left (1+\frac {1}{3} x -\frac {1}{15} x^{2}+\frac {1}{35} x^{3}-\frac {1}{63} x^{4}+\frac {1}{99} x^{5}-\frac {1}{143} x^{6}+\frac {1}{195} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \sqrt {x}+c_{1} \left (1+x +\mathrm {O}\left (x^{8}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 67
AsymptoticDSolveValue[2*x*(x+1)*y''[x]+3*(x+1)*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^7}{195}-\frac {x^6}{143}+\frac {x^5}{99}-\frac {x^4}{63}+\frac {x^3}{35}-\frac {x^2}{15}+\frac {x}{3}+1\right )+\frac {c_2 (x+1)}{\sqrt {x}} \]