29.2.5 problem 30

Internal problem ID [4638]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 30
Date solved : Monday, January 27, 2025 at 09:28:59 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: 15

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

\[ y \left (x \right ) = -\frac {2 \cos \left (x \right )^{2}}{3}+\sec \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {2 \cos ^2(x)}{3}+c_1 \sec (x) \]