Internal problem ID [4739]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.24 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 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: 38
Order:=6; dsolve(x*(x+2)*diff(y(x),x$2)+(x+1)*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+\frac {5}{4} x +\frac {7}{32} x^{2}-\frac {3}{128} x^{3}+\frac {11}{2048} x^{4}-\frac {13}{8192} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+4 x +2 x^{2}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 60
AsymptoticDSolveValue[x*(x+2)*y''[x]+(x+1)*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (2 x^2+4 x+1\right )+c_1 \sqrt {x} \left (-\frac {13 x^5}{8192}+\frac {11 x^4}{2048}-\frac {3 x^3}{128}+\frac {7 x^2}{32}+\frac {5 x}{4}+1\right ) \]