75.4.3 problem 48

Internal problem ID [16705]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 48
Date solved : Tuesday, January 28, 2025 at 09:18:51 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 6

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 7

DSolve[{D[y[x],x]*Sin[x]-y[x]*Cos[x]==0,{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (x) \]