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The following differential equation is yy''+(y''')2 + xy' = yx2 Where y' = \(\rm \frac {dy}{dx}\), y" = \(\rm \frac {d^2y}{dx^2}\) and y"' = \(\rm \frac {d^3y}{dx^3}\)

The following differential equation is yy''+(y''')2 + xy' = yx2 Where y' = \(\rm \frac {dy}{dx}\), y" = \(\rm \frac {d^2y}{dx^2}\) and y"' = \(\rm \frac {d^3y}{dx^3}\) Correct Answer Non-linear with degree 2

Concept:

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

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

A differential equation is said to be linear when

  • Dependent variable and its derivative should have power ‘1’.
  • Dependent variable and its derivatives can have product with independent variable.
  • Dependent variable and its derivatives can’t have product.

Calculation:

Given differential equation is

yy''+(y''')2 + xy' = yx2

Here x is the independent variable

y is the dependent variable

Highest derivate is y'''

So, the order of the given differential equation = 3

The power of the highest derivate = 2

So, the degree of the given differential equation = 2

∵ The derivative has the power 2, so the equation is non-linear

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