Internal problem ID [6467]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } x^{2}+y-8 \sqrt {x}\, \left (1+\ln \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(4*x^2*diff(y(x),x$2)+ y(x) = 8*sqrt(x)*(1+ln(x)),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{2}+\sqrt {x}\, \ln \relax (x ) c_{1}+\frac {\sqrt {x}\, \ln \relax (x )^{2} \left (3+\ln \relax (x )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 35
DSolve[4*x^2*y''[x]+y[x] == 8*Sqrt[x]*(1+Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \sqrt {x} (\log (x) (2 \log (x) (\log (x)+3)+3 c_2)+6 c_1) \\ \end{align*}