40.2.26 problem 52

Internal problem ID [6604]
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
Date solved : Tuesday, January 28, 2025 at 03:10:16 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.045 (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)
 

\[ y = \arcsin \left (\frac {9 \operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{-\frac {1}{3}-\frac {8 x}{9}}}{9}\right )}{8}+\frac {3}{8}+\frac {x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 60.476 (sec). Leaf size: 73

DSolve[(x-2*Sin[y[x]]+3)+(2*x-4*Sin[y[x]]-3)*Cos[y[x]]*D[y[x],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*}