Internal problem ID [2438]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.5. page
771
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x \cos \relax (x ) y^{\prime }-2 \,{\mathrm e}^{x} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 389
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*cos(x)*diff(y(x),x)-2*exp(x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{-\sqrt {2}} \left (1-2 \frac {1}{-1+2 \sqrt {2}} x +\frac {-5 \sqrt {2}+14}{40-24 \sqrt {2}} x^{2}+\frac {-122+75 \sqrt {2}}{684 \sqrt {2}-972} x^{3}+\frac {-1626 \sqrt {2}+2375}{52992-37440 \sqrt {2}} x^{4}+\frac {-75763+52810 \sqrt {2}}{3664800 \sqrt {2}-5184000} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x^{\sqrt {2}} \left (1+2 \frac {1}{1+2 \sqrt {2}} x +\frac {5 \sqrt {2}+14}{40+24 \sqrt {2}} x^{2}+\frac {122+75 \sqrt {2}}{684 \sqrt {2}+972} x^{3}+\frac {1626 \sqrt {2}+2375}{52992+37440 \sqrt {2}} x^{4}+\frac {75763+52810 \sqrt {2}}{3664800 \sqrt {2}+5184000} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 2210
AsymptoticDSolveValue[x^2*y''[x]+x*Cos[x]*y'[x]-2*Exp[x]*y[x]==0,y[x],{x,0,5}]
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