69.1.52 problem 71

Internal problem ID [14205]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 71
Date solved : Tuesday, January 28, 2025 at 06:21:48 AM
CAS classification : [_Bernoulli]

\begin{align*} y-y^{\prime } \cos \left (x \right )&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(y(x)-diff(y(x),x)*cos(x)=y(x)^2*cos(x)*(1-sin(x)),y(x), singsol=all)
 

\[ y = \frac {\cos \left (x \right )+\sin \left (x \right )+1}{\left (\sin \left (x \right )+c_{1} \right ) \left (-\sin \left (x \right )+\cos \left (x \right )+1\right )} \]

✓ Solution by Mathematica

Time used: 0.439 (sec). Leaf size: 41

DSolve[y[x]-D[y[x],x]*Cos[x]==y[x]^2*Cos[x]*(1-Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}}{\cos (x) e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}+c_1} \\ y(x)\to 0 \\ \end{align*}