Question

dy
Find
dx
if
sin x + x?
9.
cot 2x​

Answer 1

Answer:

$ANSWER</p><p></p><p>dxdy−3ycotx=sin2x</p><p>This is a linear equation of the form dxdy+Py=Q</p><p>Where P=−3cotx,Q=sin2x</p><p>∴I.F.=e∫pdx</p><p>I.F.=e∫−3cotxdx=e−3∫cotxdx</p><p>=e−3logsinx=elog(sinx)−3</p><p>=(sinx)−3=sin3x1</p><p>∴ Its solution is y.(I.F.)=∫Q(I.F.)dx</p><p></p><p>y.sin3xa=∫sin2x.sin3x1dx</p><p></p><p>sin3xy=∫sin3x2sinx.cosxdx</p><p></p><p>sin3xy=2∫cosec x.cotx.dx</p><p></p><p>sin3xy=−2cosec x+c</p><p></p><p>Putting y=2,x=π/2,         sin32π2=−2cosec (2π)+c</p><p></p><p>2=−2+c⇒c=4</p><p>∴sin3xy=−sinx2+4</p><p>y=−2sin2x+4sin3x</p><p></p><p></p><p>$

Step-by-step explanation:

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Answer 2

Answer:

y=sinx+x

dy/dx=cosx+1

y=cot2x

dy/dx=2.cosec^2 2x