60.3.209 problem 1213

Internal problem ID [11219]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1213
Date solved : Tuesday, January 28, 2025 at 05:41:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 53

dsolve(x^2*diff(diff(y(x),x),x)+(x^3+1)*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = x^{{3}/{2}} {\mathrm e}^{-\frac {x^{3}}{6}} \left (c_{1} \operatorname {BesselI}\left (-\frac {1}{6}, \frac {x^{3}}{6}\right )+c_{1} \operatorname {BesselI}\left (\frac {5}{6}, \frac {x^{3}}{6}\right )-c_{2} \left (-\operatorname {BesselK}\left (\frac {5}{6}, \frac {x^{3}}{6}\right )+\operatorname {BesselK}\left (\frac {1}{6}, \frac {x^{3}}{6}\right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 54

DSolve[-y[x] + x*(1 + x^3)*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt [3]{3} c_1 \operatorname {Hypergeometric1F1}\left (-\frac {1}{3},\frac {1}{3},-\frac {x^3}{3}\right )}{x}+\frac {c_2 x \operatorname {Hypergeometric1F1}\left (\frac {1}{3},\frac {5}{3},-\frac {x^3}{3}\right )}{\sqrt [3]{3}} \]