29.2.6 problem 31

Internal problem ID [4639]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 31
Date solved : Monday, January 27, 2025 at 09:29:02 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(y(x),x) = sin(2*x)-y(x)*tan(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 15

DSolve[D[y[x],x]==Sin[2*x]-y[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) (-2 \cos (x)+c_1) \]