38.2.12 problem 12

Internal problem ID [6441]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:04:14 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \left (-\ln \left (\cos \left (x \right )\right )+c_1 \right ) \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 16

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

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