75.12.3 problem 277

Internal problem ID [16869]
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 : 277
Date solved : Tuesday, January 28, 2025 at 09:36:08 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.172 (sec). Leaf size: 49

dsolve(diff(y(x),x)+y(x)*cos(x)=y(x)^n*sin(2*x),y(x), singsol=all)
 

\[ y = \left (\frac {{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} n -{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} +2 n \sin \left (x \right )-2 \sin \left (x \right )+2}{n -1}\right )^{-\frac {1}{n -1}} \]

✓ Solution by Mathematica

Time used: 13.167 (sec). Leaf size: 73

DSolve[D[y[x],x]+y[x]*Cos[x]==y[x]^n*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (\exp \left (-\left ((n-1) \int _1^x-\cos (K[1])dK[1]\right )\right ) \left (-(n-1) \int _1^x\exp \left ((n-1) \int _1^{K[2]}-\cos (K[1])dK[1]\right ) \sin (2 K[2])dK[2]+c_1\right )\right ){}^{\frac {1}{1-n}} \]