60.4.59 problem 1509

Internal problem ID [11510]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1509
Date solved : Tuesday, January 28, 2025 at 06:06:42 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 29

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+(4*x^3+(-4*nu^2+1)*x)*diff(y(x),x)+(4*nu^2-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 33

DSolve[(-1 + 4*nu^2)*y[x] + ((1 - 4*nu^2)*x + 4*x^3)*D[y[x],x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_1 \operatorname {BesselJ}(\nu ,x)^2+c_3 \operatorname {BesselY}(\nu ,x)^2+c_2 \operatorname {BesselJ}(\nu ,x) \operatorname {BesselY}(\nu ,x)\right ) \]