29.26.4 problem 737

Internal problem ID [5325]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 737
Date solved : Monday, January 27, 2025 at 11:13:21 AM
CAS classification : [_exact]

\begin{align*} \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{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 43

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)
 

\[ y \left (x \right ) = \frac {-b x +\operatorname {RootOf}\left (2 x \,a^{2}-2 b^{2} x -\pi a -2 \arcsin \left (\sin \left (\textit {\_Z} \right )+c_{1} \right ) a +2 \textit {\_Z} b \right )}{a} \]

✓ Solution by Mathematica

Time used: 0.661 (sec). Leaf size: 50

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

\[ \text {Solve}[\sin (a x) \sin (b y(x))-\cos (a x) \cos (b y(x))-\sin (b x) \cos (a y(x))-\cos (b x) \sin (a y(x))=c_1,y(x)] \]