60.3.65 problem 1066

Internal problem ID [11075]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1066
Date solved : Monday, January 27, 2025 at 10:44:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.156 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 1.199 (sec). Leaf size: 37

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

\[ y(x)\to c_1 \cosh \left (\sqrt {-\sin ^2(x)}\right )+i c_2 \sinh \left (\sqrt {-\sin ^2(x)}\right ) \]