60.3.131 problem 1135

Internal problem ID [11141]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1135
Date solved : Monday, January 27, 2025 at 10:46:48 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y = c_{1} \sinh \left (\sqrt {x}\right )+c_{2} \cosh \left (\sqrt {x}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

DSolve[-y[x] + 2*D[y[x],x] + 4*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh \left (\sqrt {x}\right )+i c_2 \sinh \left (\sqrt {x}\right ) \]