Internal problem ID [15161]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 299.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve(y(x)*cos(x)+(2*y(x)-sin(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {\sin \left (x \right )}{2 \operatorname {LambertW}\left (-\frac {\sin \left (x \right ) {\mathrm e}^{\frac {c_{1}}{2}}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 10.969 (sec). Leaf size: 349
DSolve[y[x]*Cos[x]+(2*y[x]-Sin[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {\sqrt [3]{-2} \left (\frac {2^{2/3} \cos (x) (4 y(x)+\sin (x))}{\sqrt [3]{-\cos ^3(x)} (\sin (x)-2 y(x))}+(-2)^{2/3}\right ) \left (\frac {\left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) (4 y(x)+\sin (x))}{\sqrt [3]{2} (\sin (x)-2 y(x))}+(-2)^{2/3}\right ) \left (-\log \left (\frac {2^{2/3} \cos (x) (4 y(x)+\sin (x))}{\sqrt [3]{-\cos ^3(x)} (\sin (x)-2 y(x))}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} \left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) (4 y(x)+\sin (x))}{\sin (x)-2 y(x)}+1\right )+\left (\frac {\sqrt [3]{-1} \left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) (4 y(x)+\sin (x))}{\sin (x)-2 y(x)}+1\right ) \log \left (\frac {2^{2/3} \left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) (4 y(x)+\sin (x))}{\sin (x)-2 y(x)}+2 (-2)^{2/3}\right )+3\right )}{9 \left (\frac {(4 y(x)+\sin (x))^3}{(\sin (x)-2 y(x))^3}-\frac {3 \sqrt [3]{-1} \cos (x) (4 y(x)+\sin (x))}{\sqrt [3]{-\cos ^3(x)} (\sin (x)-2 y(x))}+2\right )}=\frac {1}{9} 2^{2/3} \left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) \log (\sin (x))+c_1,y(x)\right ] \]