Internal problem ID [5261]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {-2 \sin \left (y\right )+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }=-x -3} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
dsolve((x-2*sin(y(x))+3)+(2*x-4*sin(y(x))-3)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \arcsin \left (\frac {9 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {8 x}{9}} {\mathrm e}^{-\frac {1}{3}} c_{1}}{9}\right )}{8}+\frac {x}{2}+\frac {3}{8}\right ) \]
✓ Solution by Mathematica
Time used: 60.95 (sec). Leaf size: 73
DSolve[(x-2*Sin[y[x]]+3)+(2*x-4*Sin[y[x]]-3)*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {1}{8} \left (9 W\left (-\frac {1}{9} e^{-\frac {2}{9} (4 x+3-8 c_1)}\right )+4 x+3\right )\right ) y(x)\to \arcsin \left (\frac {1}{8} \left (9 W\left (-\frac {1}{9} e^{-\frac {2}{9} (4 x+3-8 c_1)}\right )+4 x+3\right )\right ) \end{align*}