The given differential equation by separation of variables wil be cosy = -1/2 sin2x + C.
An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.
The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves. They can also be for multiple variables.
The given differential equation is
csc(y) dx = sec2(x) dy
We know that
csc(y) = 1/ siny
sec(x) = 1/ cosx
Also we can write it;
dx/siny = dy/cos2x
Cross multiplication, by separation of variables.
siny dy = cos2x dx
On diffrientiate;
cosy = -1/2 sin2x + C
Hence, The given differential equation by separation of variables wil be cosy = -1/2 sin2x + C.
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