The differential equation of the family of curves y-a cos x-b is -MP PET 1993-A- d 2 y - dx 2- y -0B- d 2 y - dx 2- y -0C- d 2 y - dx 2-2 y -0D- None of these

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Formation of a Differential Equation from a General Solution

The different...

Question

The differential equation of the family of curves $y = a c o s (x + b)$ is

[MP PET 1993]

$\frac{d^{2} y}{d x^{2}} - y = 0$

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$\frac{d^{2} y}{d x^{2}} + y = 0$

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$\frac{d^{2} y}{d x^{2}} + 2 y = 0$

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None of these

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Solution

The correct option is B
$\frac{d^{2} y}{d x^{2}} + y = 0$

Given equation y = a cos (x + b)
Differentiate it w.r.t x we get $\frac{d y}{d x} = - a s i n (x + b)$
Again $\frac{d^{2} y}{d x^{2}} = - a c o s (x + b) = - y o r \frac{d^{2} y}{d x^{2}} + y = 0.$

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The differential equation of the family of curves y=a cos(x+b) is [MP PET 1993]

The correct option is B d2ydx2+y=0 Given equation y = a cos (x + b) Differentiate it w.r.t x we get dydx=−a sin (x+b) Again d2ydx2=−a cos (x+b)=−y or d2ydx2+y=0.

The differential equation of the family of curves $y = a c o s (x + b)$ is

[MP PET 1993]

The correct option is B
$\frac{d^{2} y}{d x^{2}} + y = 0$

Given equation y = a cos (x + b)
Differentiate it w.r.t x we get $\frac{d y}{d x} = - a s i n (x + b)$
Again $\frac{d^{2} y}{d x^{2}} = - a c o s (x + b) = - y o r \frac{d^{2} y}{d x^{2}} + y = 0.$