3.283 problem 1288

Internal problem ID [9617]

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]]

\[ \boxed {16 x^{2} y^{\prime \prime }+\left (4 x +3\right ) y=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 21

dsolve(16*x^2*diff(diff(y(x),x),x)+(4*x+3)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x^{\frac {1}{4}} \left (c_{1} \sin \left (\sqrt {x}\right )+c_{2} \cos \left (\sqrt {x}\right )\right ) \]

Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 43

DSolve[(3 + 4*x)*y[x] + 16*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right ) \]