Internal problem ID [6737]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 75
dsolve((x^2+3)*diff(y(x),x$2)-7*x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{4}-9 x^{2}+\frac {27}{8}\right )+c_{2} \left (\frac {\left (96 x^{4}-864 x^{2}+324\right ) \ln \left (\sqrt {x^{2}+3}-x \right )}{6144}+\frac {\left (200 x^{3}-660 x \right ) \sqrt {x^{2}+3}}{6144}+\frac {25 x^{4}}{768}-\frac {75 x^{2}}{256}+\frac {225}{2048}\right ) \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 207
DSolve[(x^2+3)*y''[x]-7*x*y'[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (3 c_2 \left (8 x^4-72 x^2+27\right ) \left (-60 \text {RootSum}\left [7838208000 \text {$\#$1}^4-188281584000 \text {$\#$1}^2-241544908800 \text {$\#$1}+18453344881\&,\text {$\#$1} \log \left (-1080 \text {$\#$1} (7560 \text {$\#$1} (50430777480 \text {$\#$1}+20338927421)-9387688727006587)+868082003147887664 x \left (\sqrt {x^2+3}-x\right )+15417510572689690113\right )\&\right ]-24300 \text {RootSum}\left [210880720572480000000 \text {$\#$1}^4-30882886815600000 \text {$\#$1}^2+97825688064000 \text {$\#$1}+18453344881\&,\text {$\#$1} \log \left (437400 \text {$\#$1} (3061800 \text {$\#$1} (20424464879400 \text {$\#$1}-20338927421)-9387688727006587)+868082003147887664 x \left (\sqrt {x^2+3}-x\right )+15417510572689690113\right )\&\right ]+\tanh ^{-1}\left (\frac {x}{\sqrt {x^2+3}}\right )\right )+165 c_2 \sqrt {x^2+3} x+3 c_1 \left (8 x^4-72 x^2+27\right )-50 c_2 \sqrt {x^2+3} x^3\right ) \\ \end{align*}