12.6.21 problem 21

Internal problem ID [1700]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 21
Date solved : Monday, January 27, 2025 at 05:30:52 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([(sin(x)-y(x)*sin(x)-2*cos(x))+(cos(x))*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y = 2 \tan \left (x \right )+1 \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 11

DSolve[{(Sin[x]-y[x]*Sin[x]-2*Cos[x])+(Cos[x])*D[y[x],x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \tan (x)+1 \]