60.3.66 problem 1067

Internal problem ID [11076]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1067
Date solved : Monday, January 27, 2025 at 10:44:20 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: 0.041 (sec). Leaf size: 17

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

\[ y = c_{1} {\mathrm e}^{\sin \left (x \right )}+c_{2} {\mathrm e}^{-\sin \left (x \right )} \]

✓ Solution by Mathematica

Time used: 2.778 (sec). Leaf size: 34

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

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