60.3.313 problem 1319

Internal problem ID [11323]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1319
Date solved : Monday, January 27, 2025 at 11:13:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.152 (sec). Leaf size: 31

dsolve(x*(x^2+2)*diff(diff(y(x),x),x)-diff(y(x),x)-6*x*y(x)=0,y(x), singsol=all)
 

\[ y = \left (x^{2}+2\right )^{{3}/{4}} \left (c_{1} x^{{3}/{2}}+\operatorname {hypergeom}\left (\left [-\frac {3}{4}, \frac {7}{4}\right ], \left [\frac {1}{4}\right ], -\frac {x^{2}}{2}\right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 109

DSolve[-6*x*y[x] - D[y[x],x] + x*(2 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {6 K[1]^2+5}{2 K[1]^3+4 K[1]}dK[1]-\frac {1}{2} \int _1^x-\frac {1}{K[2]^3+2 K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {6 K[1]^2+5}{2 K[1]^3+4 K[1]}dK[1]\right )dK[3]+c_1\right ) \]