The differential equation \(\rm {\left(dy\over dx\right)}^2 - xy = x^

1.	The differential equation \(\rm {\left(dy\over dx\right)}^2 - xy = x^3y^4\)1. Linear of degree 4 and order 32. Non-linear of degree 2 and order 13. Linear of degree 2 and order 14. Non-linear of degree 4 and order 3
Answer» Correct Answer - Option 2 : Non-linear of degree 2 and order 1 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 \(\rm {\left(dy\over dx\right)}^2 - xy = x^3y^4\) Here x is the independent variable y is the dependent variable Highest derivate is \(\rm dy\over dx\) So, the order of the given differential equation = 1 The power of the highest derivate = 2 So, the degree of the given differential equation = 2 As the power of is 2 it is non-linear

The differential equation \(\rm {\left(dy\over dx\right)}^2 - xy = x^3y^4\)1. Linear of degree 4 and order 32. Non-linear of degree 2 and order 13. Linear of degree 2 and order 14. Non-linear of degree 4 and order 3

Answer» Correct Answer - Option 2 : Non-linear of degree 2 and order 1

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

\(\rm {\left(dy\over dx\right)}^2 - xy = x^3y^4\)

Here x is the independent variable

y is the dependent variable

Highest derivate is \(\rm dy\over dx\)

So, the order of the given differential equation = 1

The power of the highest derivate = 2

So, the degree of the given differential equation = 2

As the power of is 2 it is non-linear

The differential equation \(\rm {\left(dy\over dx\right)}^2 - xy = x^3y^4\)1. Linear of degree 4 and order 32. Non-linear of degree 2 and order 13. Linear of degree 2 and order 14. Non-linear of degree 4 and order 3

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