Differential Equations Quiz

What is the definition of a separable differential equation?

• An equation containing the derivatives of one or more unknown functions with respect to one or more independent variables

• A differential equation with separable variables

• A differential equation where the unknown function depends on only one independent variable

• An nth-order ordinary differential equation in one dependent variable

Which of the following is a method of solution for separable differential equations?

• Method of separation of variables

• Runge-Kutta method

• Method of undetermined coefficients

• Euler's method

What is the definition of a homogeneous function?

• A function that is separable

• A function that is linear in nature

• A function that contains only one independent variable

• A function that satisfies the property f(x,y) = f(tx,ty) for all t

Which of the following is an example of a homogeneous differential equation?

• y' = y - xy

• xy' + y = 1

• y' = sin(2x)

• y' = y - x

What is the theorem related to the existence of a unique solution for initial value problems?

• Rolle's Theorem

• Cauchy's Existence Theorem

• Picard-Lindelöf Theorem

• Euler's Theorem

What is the method of solution for homogeneous differential equations?

• Linear Differential Equation

• Method of Solution of Homogeneous Differential Equation

• Exact differential equation

• Separable differential equation

What is the integrating factor for non exact differential equations?

• $e^{(1-n)p(x)dx}$

• $e^{(1-3)p(x)dx}$

• $e^{(1-5)p(x)dx}$

• $e^{(1-2)p(x)dx}$

Which function is considered a homogeneous function of degree δ?

• $f(x,y) = x + ny$

• $f(x,y) = x^2 + y^2$

• $f(x,y) = x + \ln y$

• $f(x,y) = y^2$

What is the solution method for Bernoulli differential equations?

• Orthogonal trajectories

• Linear Differential Equation

• Separable differential equation

• Method of Solution of Homogeneous Differential Equation

What are the orthogonal trajectories of the family of curves $y = x + c$?

• $y = -x + c*$

• $y = x - c$

• $y = -x + c$

• $y = x + c*$