Internal problem ID [7661]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 173.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(4*x^2*(1+x)*diff(y(x),x$2)+4*x*(3+8*x)*diff(y(x),x)-(5-49*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {x}}{\left (x +1\right )^{4}}+\frac {c_{2} \left (6 x^{3} \ln \left (x \right )-18 x^{2}-9 x -2\right )}{6 \left (x +1\right )^{4} x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 52
DSolve[4*x^2*(1+x)*y''[x]+4*x*(3+8*x)*y'[x]-(5-49*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {6 c_1 x^3+6 c_2 x^3 \log (x)-18 c_2 x^2-9 c_2 x-2 c_2}{6 x^{5/2} (x+1)^4} \]