58.2.14 problem 15

Internal problem ID [9137]
Book : Second order enumerated odes
Section : section 2
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:48:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 51

dsolve(diff(diff(y(x),x),x)-2/x^2*y(x) = x*exp(-x^(1/2)),y(x), singsol=all)
 

\[ y = \frac {4 \,{\mathrm e}^{-\sqrt {x}} \left (7 x^{{5}/{2}}+140 x^{{3}/{2}}+x^{3}+35 x^{2}+840 \sqrt {x}+420 x +840\right )+c_{1} x^{3}+c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 57

DSolve[D[y[x],{x,2}]-2/x^2*y[x] == x*Exp[-x^(1/2)],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \int _1^x\frac {1}{3} e^{-\sqrt {K[1]}}dK[1]+c_2 x^2+\frac {2 \Gamma \left (8,\sqrt {x}\right )}{3 x}+\frac {c_1}{x} \]