Internal problem ID [3473]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 737.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 36
dsolve((a*cos(b*x+a*y(x))-b*sin(a*x+b*y(x)))*diff(y(x),x)+b*cos(b*x+a*y(x))-a*sin(a*x+b*y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-a x +\RootOf \left (-a^{2} x +b^{2} x +\arcsin \left (\cos \left (\textit {\_Z} \right )+c_{1}\right ) b +a \textit {\_Z} \right )}{b} \]
✓ Solution by Mathematica
Time used: 0.743 (sec). Leaf size: 50
DSolve[(a Cos[b x+a y[x]]-b Sin[a x+ b y[x]])y'[x]+b Cos[b x+a y[x]]-a Sin[a x+b y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\sin (a x) \sin (b y(x))-\cos (a x) \cos (b y(x))-\sin (b x) \cos (a y(x))-\cos (b x) \sin (a y(x))=c_1,y(x)] \]