60.3.391 problem 1397

Internal problem ID [11401]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1397
Date solved : Monday, January 27, 2025 at 11:19:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(diff(y(x),x),x) = -1/x^4*diff(y(x),x)+1/x^5*y(x),y(x), singsol=all)
 

\[ y = x \left (-3 c_{2} \Gamma \left (\frac {1}{3}, -\frac {1}{3 x^{3}}\right ) \Gamma \left (\frac {2}{3}\right )+2 c_{2} \sqrt {3}\, \pi +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}] == y[x]/x^5 - D[y[x],x]/x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \Gamma \left (\frac {1}{3},-\frac {1}{3 x^3}\right )}{3^{2/3} \sqrt [3]{-\frac {1}{x^3}}}+c_1 x \]