1.347 problem 348

Internal problem ID [8684]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 348.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact]

\[ \boxed {\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right )+\sin \left (y\right )=0} \]

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 15

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

\[ y \left (x \right ) \sin \left (x \right )+x \sin \left (y \left (x \right )\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 17

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

\[ \text {Solve}[x \sin (y(x))+y(x) \sin (x)=c_1,y(x)] \]