60.3.213 problem 1217

Internal problem ID [11223]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1217
Date solved : Tuesday, January 28, 2025 at 05:42:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

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

\[ y = \sec \left (x \right ) \left (c_{1} \operatorname {BesselJ}\left (\sqrt {a}, x\right )+c_{2} \operatorname {BesselY}\left (\sqrt {a}, x\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 29

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

\[ y(x)\to \sec (x) \left (c_1 \operatorname {BesselJ}\left (\sqrt {a},x\right )+c_2 \operatorname {BesselY}\left (\sqrt {a},x\right )\right ) \]