Internal problem ID [6699]
Book: Second order enumerated odes
Section: section 2
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {2 y}{x^{2}}-x \,{\mathrm e}^{-\sqrt {x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 54
dsolve(diff(diff(y(x),x),x)-2/x^2*y(x) = x*exp(-x^(1/2)),y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\frac {c_{1}}{x}+\frac {4 \,{\mathrm e}^{-\sqrt {x}} \left (7 x^{\frac {5}{2}}+140 x^{\frac {3}{2}}+x^{3}+35 x^{2}+840 \sqrt {x}+420 x +840\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 53
DSolve[y''[x]-2/x^2*y[x] == x*Exp[-x^(1/2)],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \text {Gamma}\left (8,\sqrt {x}\right )+3 \left (c_2 x^3+c_1\right )-2 e^{-\sqrt {x}} \left (x^{7/2}+x^3\right )}{3 x} \\ \end{align*}