Internal problem ID [5315]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (t).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\sin \left (y\right )-\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 25
dsolve((1+sin(y(x)))=(2*y(x)*cos(y(x))-x*(sec(y(x))+tan(y(x))) )*diff(y(x),x),y(x), singsol=all)
\[ x +\frac {-y \left (x \right )^{2}-c_{1}}{\sec \left (y \left (x \right )\right )+\tan \left (y \left (x \right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 1.489 (sec). Leaf size: 66
DSolve[(1+Sin[y[x]])==(2*y[x]*Cos[y[x]]-x*(Sec[y[x]]+Tan[y[x]]) )*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {3 \pi }{2} \\ \text {Solve}\left [x&=y(x)^2 e^{-2 \text {arctanh}\left (\tan \left (\frac {y(x)}{2}\right )\right )}+c_1 e^{-2 \text {arctanh}\left (\tan \left (\frac {y(x)}{2}\right )\right )},y(x)\right ] \\ y(x)\to -\frac {\pi }{2} \\ \end{align*}