Internal problem ID [4727]
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: 3.5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([(x-1)*(x-2)*diff(y(x),x$2)+(4*x-6)*diff(y(x),x)+2*y(x)=0,y(0) = 2, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = 2+x +\frac {1}{2} x^{2}+\frac {1}{4} x^{3}+\frac {1}{8} x^{4}+\frac {1}{16} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 34
AsymptoticDSolveValue[{(x-1)*(x-2)*y''[x]+(4*x-6)*y'[x]+2*y[x]==0,{y[0]==2,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{16}+\frac {x^4}{8}+\frac {x^3}{4}+\frac {x^2}{2}+x+2 \]