question 2 Determine the order of the given differential equation, also state wh

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question 2

Determine the order of the given differential equation, also state whether it is linear or nonlinear (1 + y^2) d^2y/dx^2 + x dy/dx + y = e^x d^3y/dt^3 + t dy/dt + (cos^2 t)y = t^3 3 sin t = (1 - t^2)y' - ty Solve the following first order differential equations with a proper technique, find an explicit solution whenever possible. If you use the technique for exact equations, then show why the equation is exact. Show all your work for each question you solved. (x^2 + 1)dy/dx + 3xy = 6x y' + 3x^2 y = x^2 e^3x^2

Explanation / Answer

The number of the highest derivative in a differential equation is called the order of differential equation

a)
order = 2
because there is a term of d^2y/dx^2

Its non linear

b)
order = 3
because there is a term of d^3y/dx^3

Its non linear

c)
order = 1
because there is a term of y'

Its non linear

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