Geometrical Applications of Differential Equations
The equation ...
Question
The equation y2exy=9e−3⋅x2 defines y as a differentiable function of x. The value of dydx for x=−1 and y=3 is
A
−152
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B
−95
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C
3
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D
15
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Solution
The correct option is D15 y2exy=9e−3⋅x2
Using product rule of differentiation, y2(exy(xdydx+y))+exy⋅2ydydx=9e−3⋅2x
Putting x=−1 and y=3 9(e−3(−dydx+3))+e−3⋅6dydx=−9e−3⋅2⇒−9(dydx−3)+6dydx=−18⇒3dydx=45⇒dydx=15