Internal problem ID [3876]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 40
dsolve((n*cos(n*x+m*y(x))-m*sin(m*x+n*y(x)))+(m*cos(n*x+m*y(x))-n*sin(m*x+n*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-n x +\RootOf \left (m^{2} x -x \,n^{2}-m \pi +m \arccos \left (\sin \left (\textit {\_Z} \right )+c_{1}\right )+\textit {\_Z} n \right )}{m} \]
✓ Solution by Mathematica
Time used: 0.773 (sec). Leaf size: 50
DSolve[(n*Cos[n*x+m*y[x]]-m*Sin[m*x+n*y[x]])+(m*Cos[n*x+m*y[x]]-n*Sin[m*x+n*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\sin (m x) \sin (n y(x))-\cos (m x) \cos (n y(x))-\sin (n x) \cos (m y(x))-\cos (n x) \sin (m y(x))=c_1,y(x)] \]