60.4.52 problem 1500

Internal problem ID [11503]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1500
Date solved : Tuesday, January 28, 2025 at 06:06:40 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 114

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

\[ y = \frac {-c_{2} x^{\frac {\nu }{2}+1} \operatorname {BesselJ}\left (-\nu +1, 2 \sqrt {\nu }\, \sqrt {x}\right )-c_3 \,x^{\frac {\nu }{2}+1} \operatorname {BesselY}\left (-\nu +1, 2 \sqrt {\nu }\, \sqrt {x}\right )-x^{\frac {\nu }{2}+\frac {1}{2}} \sqrt {\nu }\, \operatorname {BesselJ}\left (-\nu , 2 \sqrt {\nu }\, \sqrt {x}\right ) c_{2} -x^{\frac {\nu }{2}+\frac {1}{2}} \sqrt {\nu }\, \operatorname {BesselY}\left (-\nu , 2 \sqrt {\nu }\, \sqrt {x}\right ) c_3 +{\mathrm e}^{x} c_{1} \sqrt {x}}{\sqrt {x}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved