Differential Equations: Variable Separable Form

The video tutorial covers methods to solve first order, first degree differential equations, focusing on the variable separable method. It explains the process of separating variables, integrating both sides, and finding general and particular solutions. Examples are provided to illustrate the method. The tutorial also explores applications in finding curve equations and in banking, where differential equations are used to calculate interest growth.

Which of the following is NOT a method to solve first order, first degree differential equations?

• Variable separable

• Linear

• Homogeneous

• Quadratic

In the variable separable method, what is the first step after identifying the type of differential equation?

• Add an arbitrary constant

• Multiply by a constant

• Separate the variables

• Differentiate both sides

What is the form of the solution obtained after integrating both sides in the variable separable method?

• H(y) = G(x) + C

• H(y) = G(x) - C

• H(y) = G(x) * C

• H(y) = G(x) / C

When finding a particular solution, what is the purpose of substituting specific values of x and y?

• To check the solution

• To simplify the equation

• To find the derivative

• To eliminate the arbitrary constant

What is the slope of the tangent to the curve at any point (x, y) if dy/dx = 4x/y^2?

• y/4x

• y^2/4x

• 4x/y^2

• 4x/y

In the context of continuous interest, what does the principal become after a certain time if it doubles?

• Half of the original

• Quadruple the original

• Triple the original

• Double the original

What is the differential equation form when the principal increases continuously at a rate of 10% per year?

• dP/dt = P/10

• dP/dt = P^2

• dP/dt = 10P

• dP/dt = 0.1P