Concept explainers
(a)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
As, here, derivative of dependent variable is multiplied with itself.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
Which is a non-linear differential equation.
As, here, derivative of dependent variable is multiplied with itself.
(b)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
As, here, derivative of dependent variable is not multiplied with itself.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
(c)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
As, here, derivative of dependent variable is not multiplied with itself.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
As, here, derivative of dependent variable is not multiplied with itself.
(d)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
is a non-linear differential equation.
As, here, derivative of dependent variable is multiplied with itself.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
Which is a non-linear differential equation.
As, here, derivative of dependent variable is multiplied with itself.
(e)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
As, here, derivative of dependent variable is multiplied with independent variable.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
Which is a non-linear differential equation.
As, here, function of dependent variable is multiplied with independent variable.
(f)
Whether the given differential equation is linear or non-linear with supportive reason.
Answer to Problem 2.1P
As, here, function of dependent variable is not multiplied with independent variable.
Explanation of Solution
Given:
Concept Used:
An ordinary differential for
where the ‘coefficient’ functions
In other words a differential equation is said to be linear if and only if the derivative of dependent variable should not be multiplied with dependent variable itself, otherwise it should be non-linear.
Calculation:
Given differential equation is
which is a linear differential equation.
As, here, function of dependent variable is not multiplied with independent variable.
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Chapter 2 Solutions
SYSTEM DYNAMICS LL+CONNECT