Form a differential equation by eliminating the arbitrary constant a from the equation. y = a sin(2x + 3).??

2 Answers
Jul 5, 2018

Answer:

#y' = 2 y cot(2x+3) #

Explanation:

#y = a sin(2x + 3) qquad bbbA#

Differentiate both sides wrt #x#:

#y' = 2a cos(2x + 3) qquad bbbB#

Use #bbbA/bbbB# to eliminate #a#

#bbbA/bbbB implies y/(y') = 1/2 tan(2x+3) qquad y' = 2 y cot(2x+3) #

That's a first-order linear ordinary differential equation, solvable by separation of variables.

Answer:

#dy/dx=2y\cot(2x+3)#

Explanation:

Given equation:

#y=a\sin(2x+3)#

differentiating above equation w.r.t. #x# as follows

#dy/dx=\frac{d}{dx}(a\sin(2x+3))#

#dy/dx=a\frac{d}{dx}(\sin(2x+3))#

#dy/dx=a\cos(2x+3)\frac{d}{dx}(2x+3)#

#dy/dx=a\cos(2x+3)(2)#

#dy/dx=2a\cos(2x+3)#

setting #a=y/\sin(2x+3)# in above D.E. as follows

#dy/dx=2(y/\sin(2x+3))\cos(2x+3)#

#dy/dx=2y\cot(2x+3)#