Internal problem ID [8868]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1288.
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}+\left (4 x +3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(16*x^2*diff(diff(y(x),x),x)+(4*x+3)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sqrt {x}\right ) x^{\frac {1}{4}}+c_{2} x^{\frac {1}{4}} \cos \left (\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 43
DSolve[(3 + 4*x)*y[x] + 16*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right ) \\ \end{align*}