75.6.23 problem 156

Internal problem ID [16779]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 156
Date solved : Tuesday, January 28, 2025 at 09:22:19 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.391 (sec). Leaf size: 6

dsolve([cos(x)*diff(y(x),x)-y(x)*sin(x)=-sin(2*x),y(1/2*Pi) = 0],y(x), singsol=all)
 

\[ y = \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.853 (sec). Leaf size: 26

DSolve[{Cos[x]*D[y[x],x]-y[x]*Sin[x]==-Sin[2*x],{y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sec (x) \int _{\frac {\pi }{2}}^x-\sin (2 K[1])dK[1] \]