60.3.68 problem 1069

Internal problem ID [11078]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1069
Date solved : Monday, January 27, 2025 at 10:44:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.226 (sec). Leaf size: 15

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

\[ y = c_{1} \sin \left (\cos \left (x \right )\right )+c_{2} \cos \left (\cos \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 1.998 (sec). Leaf size: 18

DSolve[Sin[x]^2*y[x] - Cot[x]*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (\cos (x))+c_2 \sin (\cos (x)) \]