60.3.94 problem 1098

Internal problem ID [11104]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1098
Date solved : Monday, January 27, 2025 at 10:45:49 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-y a \,x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)-y(x)*a*x^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 41

DSolve[-(a*x^3*y[x]) - D[y[x],x] + x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh \left (\frac {\sqrt {a} x^2}{2}\right )+i c_2 \sinh \left (\frac {\sqrt {a} x^2}{2}\right ) \]