3.290 problem 1290

Internal problem ID [8868]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1290.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\[ \boxed {\left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y=0} \]

Solution by Maple

Time used: 0.015 (sec). Leaf size: 29

dsolve((27*x^2+4)*diff(diff(y(x),x),x)+27*x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} \sinh \left (\frac {\operatorname {arcsinh}\left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right )+c_{2} \cosh \left (\frac {\operatorname {arcsinh}\left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right ) \]

Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 103

DSolve[-3*y[x] + 27*x*y'[x] + (4 + 27*x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \cosh \left (\frac {\sqrt {-27 x^2-4} \arctan \left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right )+i c_2 \sinh \left (\frac {\sqrt {-27 x^2-4} \arctan \left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right ) \\ \end{align*}