75.12.25 problem 299

Internal problem ID [16891]
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
Date solved : Tuesday, January 28, 2025 at 09:39:54 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.653 (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: 0.296 (sec). Leaf size: 96

DSolve[y[x]*Cos[x]+(2*y[x]-Sin[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {\left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) (\sin (x)+4 y(x))}{\sqrt [3]{2} (\sin (x)-2 y(x))}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {1}{9} 2^{2/3} \left (-\cos ^3(x)\right )^{2/3} \sec ^2(x) \log (\sin (x))+c_1,y(x)\right ] \]