In each of problems 1 through 6, determine the order of the given differential equation; alsostate whether the equation is linear or nonlinear.(1) t^2 (d^2y/dt^2)+ t(dy/dt)+ 2y = sin t(2) (1 + y^2)(d^2y/dt^2)+ t(dy/dt)+ y = e^t(3) (d^4y/dt^4)+(d^3y/dt^3)+(d^2y/dt^2) +(dy/dt)+ y =1(4) (dy/dt)+ ty^2 = 0(5) (d^2y/dt^2)+ sin(t + y) = sin t

The question is in complete, below is the complete question

"In each of Problems 1 through 6, determine the order of the given differential equation; also state whether the equation is linear or nonlinear

1.

2.

3.

4.

5.

6.

"

below is the answer

1. second order, linear  

2. second order, non- linear  

3. fourth order, linear

4. first order, non- linear

5.second order, non- linear

6. third order, linear  

Step-by-step explanation:

To determine the order of a differential equation, we look out for the highest derivative in the equation. if the power of the highest derivative is one, we call it a first order  differential equation and if the highest power of the derivative is 2 we call it a second order differential equation.

Also a differential equation is said to be linear if the independent variable and its derivative are linear.

Now let use the above condition to check the following

1.

the highest power of the derivative is 2 and the independent variable and its derivatives are linear hence we conclude second order, linear  

2.

the highest power of the derivative is 2 and the is non-linear hence we conclude second order, non- linear  

3.

the highest power of the derivative is 4 and the independent variable and its derivatives are linear hence we conclude fourth order, linear

4.

the highest power of the derivative is 1 and the is non-linear hence we conclude first order, non- linear  

5.

the highest power of the derivative is 2 and the is non-linear hence we conclude second order, non- linear  

6.

the highest power of the derivative is 3 and the independent variable and its derivatives are linear hence we conclude third order, linear  

2

step-by-2step explanation:

true

step-by-step explanation: