Internal problem ID [4035]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.22, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (y^{2}+a \sin \relax (x )\right ) y^{\prime }-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 41
dsolve((y(x)^2+a*sin(x))*diff(y(x),x)=cos(x),y(x), singsol=all)
\[ -{\mathrm e}^{-a y \relax (x )} \sin \relax (x )-\frac {\left (a^{2} y \relax (x )^{2}+2 a y \relax (x )+2\right ) {\mathrm e}^{-a y \relax (x )}}{a^{3}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.214 (sec). Leaf size: 45
DSolve[(y[x]^2+a*Sin[x])*y'[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\sin (x) \left (-e^{-a y(x)}\right )-\frac {e^{-a y(x)} \left (a^2 y(x)^2+2 a y(x)+2\right )}{a^3}=c_1,y(x)\right ] \]