Understanding Bernoulli Equations and Substitution Methods

Subtract Y from both sides

Multiply both sides by X

Divide through by X

Add Y squared to both sides

The power of Y

The power of X

The coefficient of Y

The constant term

V = Y^(1/2)

V = Y^(-2)

V = Y^(-1)

V = Y^2

Integration by parts

Separation of variables

Partial fraction decomposition

Laplace transform

1/(1+V)

e^(1+V)

V/(1+V)

ln|1+V|

Because it simplifies the equation

Because the constant C is positive

Because the equation is linear

Because it is not necessary for the solution

Y = 2/(3X + 2)

Y = 1/(3X - 1)

Y = 2/(3X - 2)

Y = 1/(3X + 1)

By setting X = 0

By using the initial condition

By solving the differential equation

By graphing the solution

It is a circle

It is a straight line

It passes through the initial condition point

It is a parabola

To verify the solution

To simplify the graph

To make the solution more readable

To eliminate the constant