16.1.15 problem 3(i)

Internal problem ID [3417]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(i)
Date solved : Monday, January 27, 2025 at 07:36:10 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

dsolve(diff(y(x),x)*sin(x)=1,y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 13

DSolve[D[y[x],x]*Sin[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\text {arctanh}(\cos (x))+c_1 \]