Question

Justify that every linear differential equations is of first degree, but the converse is not true.​

Answer 1

SOLUTION

TO JUSTIFY

Every linear differential equations is of first degree, but the converse is not true.

CONCEPT TO BE IMPLEMENTED

Differential Equation

A differential equation is an equation which involves differential coefficients or differentials

Order of Differential Equation

The order of a differential equation is the order of the highest derivative appearing in it.

Degree of Differential Equation

The degree of a differential equation is the degree of the highest derivative occuring in it after the equation has been expressed in a form free from radicals and fractions as far as the derivatives are concerned

EVALUATION

A general form of a linear differential equation is

$\displaystyle \sf{ \frac{dy}{dx} + Py = Q }$

Where P and Q are both are either functions of x or constants

The above differential equation is of first degree

Now we consider another differential equation of first degree

$\displaystyle \sf{ \frac{{d}^{2} y}{d {x}^{2} } + P \frac{dy}{dx} = Q }$

Which is of first degree but not not of first order

Thus the differential equation is not linear

Hence justified

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