Internal problem ID [14975]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } \sin \left (x \right )-y \cos \left (x \right )=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 7
DSolve[{y'[x]*Sin[x]-y[x]*Cos[x]==0,{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x) \]