Internal problem ID [9733]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1399.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\frac {\left (3 x +1\right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}+\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (3 x +5\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(diff(y(x),x),x) = 1/(x-1)*(3*x+1)/(x+1)*diff(y(x),x)-36*(x+1)^2/(x-1)^2/(3*x+5)^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x -1\right )^{\frac {3}{2}} \sqrt {3 x +5}+c_{2} \left (x -1\right )^{\frac {3}{2}} \sqrt {3 x +5}\, \left (3 \ln \left (x -1\right )+\ln \left (3 x +5\right )\right ) \]
✓ Solution by Mathematica
Time used: 2.097 (sec). Leaf size: 51
DSolve[y''[x] == (-36*(1 + x)^2*y[x])/((-1 + x)^2*(5 + 3*x)^2) + ((1 + 3*x)*y'[x])/((-1 + x)*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (1-x)^{3/2} \sqrt {3 x+5} (3 c_2 \log (1-x)+c_2 \log (3 x+5)+2 c_1) \]