58.2.15 problem 16

Internal problem ID [9138]
Book : Second order enumerated odes
Section : section 2
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:48:43 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=x \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 50

dsolve(diff(y(x),x$2)-1/sqrt(x)*diff(y(x),x)+1/(4*x^2)*(x+sqrt(x)-8)*y(x)=x,y(x), singsol=all)
 

\[ y = \frac {560 x^{{3}/{2}}+28 x^{{5}/{2}}+\left (c_{1} x^{3}+c_{2} \right ) {\mathrm e}^{\sqrt {x}}+4 x^{3}+140 x^{2}+1680 x +3360 \sqrt {x}+3360}{x} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 60

DSolve[D[y[x],{x,2}]-1/Sqrt[x]*D[y[x],x]+1/(4*x^2)*(x+Sqrt[x]-8)*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

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