Internal problem ID [2025]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\left (\sin \left (y\right )-1\right ) \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 16
dsolve(cos(y(x))*diff(y(x),x)+(sin(y(x))-1)*cos(x)=0,y(x), singsol=all)
\[ y = \arcsin \left (\frac {{\mathrm e}^{-\sin \left (x \right )}+c_{1}}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 60.309 (sec). Leaf size: 225
DSolve[Cos[y[x]]*y'[x]+(Sin[y[x]]-1)*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 \pi }{2} y(x)\to \frac {\pi }{2} y(x)\to -2 \arccos \left (-\frac {1}{8} e^{-\sin (x)} \left (c_1 e^{\frac {\sin (x)}{2}}+\sqrt {e^{\sin (x)} \left (32 e^{\sin (x)}-c_1{}^2\right )}\right )\right ) y(x)\to 2 \arccos \left (-\frac {1}{8} e^{-\sin (x)} \left (c_1 e^{\frac {\sin (x)}{2}}+\sqrt {e^{\sin (x)} \left (32 e^{\sin (x)}-c_1{}^2\right )}\right )\right ) y(x)\to -2 \arccos \left (\frac {1}{8} e^{-\sin (x)} \left (\sqrt {e^{\sin (x)} \left (32 e^{\sin (x)}-c_1{}^2\right )}-c_1 e^{\frac {\sin (x)}{2}}\right )\right ) y(x)\to 2 \arccos \left (\frac {1}{8} e^{-\sin (x)} \left (\sqrt {e^{\sin (x)} \left (32 e^{\sin (x)}-c_1{}^2\right )}-c_1 e^{\frac {\sin (x)}{2}}\right )\right ) \end{align*}