23.1.26 problem 2(p)

Internal problem ID [4116]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(p)
Date solved : Monday, January 27, 2025 at 08:36:35 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } \cos \left (x \right )+y \sin \left (x \right )&=1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 6

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

\[ y \left (x \right ) = \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 7

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

\[ y(x)\to \sin (x) \]