Question
The integrating factor of the differential equation dydx=y tan x−y2 sec x is
[MP PET 1995; Pb. CET 2002]
[MP PET 1995; Pb. CET 2002]
Answer: Option B
:
B
The differential equation
is dydx−ytanx=−y2secxI.F.=e−∫tanxdx
This is Bernoulli's equation i.e. reducible to
linear equation.
Dividing the equation by y2, we get
1y2dydx−1ytanx=−secx............(i)
Put 1y=y⇒−1y2dydx=dYdx
Equation (i) reduces to−dydx=−ytanx=−secx⇒dYdx+Ytanx=secx, Which is a linear equation
Hence I.F.=e−∫tanxdx=secx.
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:
B
The differential equation
is dydx−ytanx=−y2secxI.F.=e−∫tanxdx
This is Bernoulli's equation i.e. reducible to
linear equation.
Dividing the equation by y2, we get
1y2dydx−1ytanx=−secx............(i)
Put 1y=y⇒−1y2dydx=dYdx
Equation (i) reduces to−dydx=−ytanx=−secx⇒dYdx+Ytanx=secx, Which is a linear equation
Hence I.F.=e−∫tanxdx=secx.
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