Internal problem ID [7272]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 552.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 29
dsolve(28*x^2*(1-3*x)*diff(y(x),x$2)-7*x*(5+9*x)*diff(y(x),x)+7*(2+9*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2}}{3 x -1}+\frac {c_{2} x^{\frac {1}{4}}}{3 x -1} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 30
DSolve[28*x^2*(1-3*x)*y''[x]-7*x*(5+9*x)*y'[x]+7*(2+9*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 c_2 x^2+7 c_1 \sqrt [4]{x}}{7-21 x} \\ \end{align*}