Internal problem ID [8869]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1289.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 y^{\prime \prime } x^{2}+32 x y^{\prime }-\left (4 x +5\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 35
dsolve(16*x^2*diff(diff(y(x),x),x)+32*x*diff(y(x),x)-(4*x+5)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{\sqrt {x}} \left (\sqrt {x}-1\right )}{x^{\frac {5}{4}}}+\frac {c_{2} {\mathrm e}^{-\sqrt {x}} \left (\sqrt {x}+1\right )}{x^{\frac {5}{4}}} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 51
DSolve[(-5 - 4*x)*y[x] + 32*x*y'[x] + 16*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\sqrt {x}} \left (c_1 e^{2 \sqrt {x}} \left (\sqrt {x}-1\right )-c_2 \left (\sqrt {x}+1\right )\right )}{x^{5/4}} \\ \end{align*}