29.15.4 problem 412

Internal problem ID [5010]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 412
Date solved : Monday, January 27, 2025 at 10:03:14 AM
CAS classification : [_separable]

\begin{align*} \left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 10

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

\[ y \left (x \right ) = c_{1} \left (\sin \left (x \right )-1\right ) \]

✓ Solution by Mathematica

Time used: 0.291 (sec). Leaf size: 18

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

\begin{align*} y(x)\to -c_1 (\sin (x)-1) \\ y(x)\to 0 \\ \end{align*}