Internal problem ID [7858]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 278.
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}+4 \sin \relax (x )\right ) y^{\prime }-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 33
dsolve((y(x)^2+4*sin(x))*diff(y(x),x)-cos(x)=0,y(x), singsol=all)
\[ -{\mathrm e}^{-4 y \relax (x )} \sin \relax (x )-\frac {\left (8 y \relax (x )^{2}+4 y \relax (x )+1\right ) {\mathrm e}^{-4 y \relax (x )}}{32}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 39
DSolve[(y[x]^2+4*Sin[x])*y'[x]-Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [-\frac {1}{32} e^{-4 y(x)} \left (8 y(x)^2+4 y(x)+1\right )-e^{-4 y(x)} \sin (x)=c_1,y(x)\right ] \]