60.3.58 problem 1059

Internal problem ID [11068]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1059
Date solved : Monday, January 27, 2025 at 10:43:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 63

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

\[ y = \frac {{\mathrm e}^{-\frac {x^{5}}{5}} \left (\frac {9 c_{2} 5^{{3}/{5}} \left (x^{5}\right )^{{2}/{5}} \left (x^{5}+4\right )}{25}+x^{3} \left ({\mathrm e}^{\frac {x^{5}}{10}} \operatorname {WhittakerM}\left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right ) x^{2} c_{2} +{\mathrm e}^{\frac {x^{5}}{5}} c_{1} \right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 39

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

\[ y(x)\to c_1 x-\frac {c_2 \sqrt [5]{x^5} \Gamma \left (-\frac {1}{5},\frac {x^5}{5}\right )}{5 \sqrt [5]{5}} \]