Internal problem ID [6700]
Book: Second order enumerated odes
Section: section 2
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
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)
\[ y \relax (x ) = \frac {{\mathrm e}^{\sqrt {x}} c_{2}}{x}+{\mathrm e}^{\sqrt {x}} x^{2} c_{1}+\frac {28 x^{\frac {5}{2}}+560 x^{\frac {3}{2}}+4 x^{3}+140 x^{2}+3360 \sqrt {x}+1680 x +3360}{x} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 52
DSolve[y''[x]-1/Sqrt[x]*y'[x]+1/(4*x^2)*(x+Sqrt[x]-8)*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 \left (x^{7/2}+x^3\right )+e^{\sqrt {x}} \left (2 \text {Gamma}\left (8,\sqrt {x}\right )+c_2 x^3+3 c_1\right )}{3 x} \\ \end{align*}