Pick the TRUE statement1. $\rm x{dy\over dx} + {d^2y\over dx^2} = y$

1.	Pick the TRUE statement1. \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) is linear differential equation of order 22. \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) is non linear differential equation of order 23. \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) is non linear differential equation of degree 24. \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) is linear differential equation of degree 1
Answer» Correct Answer - Option 2 : \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) is non linear differential equation of order 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 the product with the independent variable. Dependent variable and its derivatives can’t have the product. Calculation: Given the differential equation is \(\rm x{dy\over dx} + {d^2y\over dx^2} = y\) Here x is the independent variable y is the dependent variable Highest derivate is \(\rm {d^2y\over dx^2}\) $\frac{d y}{d x}$ So, the order of the given differential equation = 2 The power of the highest derivate = 1 So, the degree of the given differential equation = 1 As the multiplication of dependent variable derivative with the independent variable, so non-linear

Pick the TRUE statement1. $\rm x{dy\over dx} + {d^2y\over dx^2} = y$ is linear differential equation of order 22. $\rm x{dy\over dx} + {d^2y\over dx^2} = y$ is non linear differential equation of order 23. $\rm x{dy\over dx} + {d^2y\over dx^2} = y$ is non linear differential equation of degree 24. $\rm x{dy\over dx} + {d^2y\over dx^2} = y$ is linear differential equation of degree 1

Answer» Correct Answer - Option 2 : $\rm x{dy\over dx} + {d^2y\over dx^2} = y$ is non linear differential equation of order 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 the product with the independent variable.
Dependent variable and its derivatives can’t have the product.

Calculation:

Given the differential equation is

$\rm x{dy\over dx} + {d^2y\over dx^2} = y$

Here x is the independent variable

y is the dependent variable

Highest derivate is $\rm {d^2y\over dx^2}$ $\frac{d y}{d x}$

So, the order of the given differential equation = 2

The power of the highest derivate = 1

So, the degree of the given differential equation = 1

As the multiplication of dependent variable derivative with the independent variable, so non-linear

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment