Question

Evaluate: ∫ tan²x dx

Find the order of differential equation: (d²y/dx²)² + cos (dy/dx) =0​

Answer 1

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We need to find the order and degree of the differential equation

$\frac{d²y}{dx²} = \sqrt{y + (\frac{dy}{dx} }) ^{2}$

$Consider \: \frac{d²y}{dx²} = \sqrt{y( \frac{dy}{dx})^{2} }$

$= > \: \frac{ {d}^{2} y}{dx} = (y + ( \frac{dy}{dx} )^{2} )^{ \frac{1}{2} }$

$[ \frac{ {d}^{2} y}{dx ^{2} } ]^{2} = y + ( \frac{dy}{dx})^{2}$

We know that, the order of a differential equation is the order of the highest order derivative present in the equation and the degree of a differential equation is the power of the highest order derivative in the equation.

Here the highest order derivative is 2 and its power is 2.

Thus order is 2 and power is 2.

Answer 2

Answer:

We know that, the order of a differential equation is the order of the highest order derivative present in the equation and the degree of a differential equation is the power of the highest order derivative in the equation.

Here the highest order derivative is 2 and its power is 2.

Thus order is 2 and power is 2.

$thanks$