Linear/Nonlinear
The formula for linear first-order derivatives is:
dy/dx+P(x)y=Q(x)
The formula for separable first-order derivatives is:
(1/g(y))dy=f(x)dx
The formula for homogenous first-order derivatives is:
dy/dx=f(y/x)
The formula for exact first-order derivatives is:
M(x,y)dx + N(x,y)dy=0
The definition of the Euler Method.
What is estimating a differential equation by calculating the tangent line at small intervals.
The three main differences between linear and nonlinear are:
y or dx/dy is raised to a power other than 1
What is the difference between separable and non- separable equations:
Separable can have variables separated to one side while non-separable cannot be rearranged into that format.
An equation is homogenous when:
All the terms are raised to the same degree
An equation is exact when:
where the partial derivative of one term with respect to y equals the partial derivative of another term with respect to x
The formula for the Euler method.
What is yn=yn-1+hF(xn-1,yn-1)?
Solve for y: dx/dy+4y=8
y=2+Ce^−4x
solve this equation: (dy)/(dx)=x⋅y
y=Ce(x^2)/2
Solve for y: dy/dx=x+y/x
y=x(ln|x|+C)
solve this equation:(2x+y)dx+(x+3y2)dy=0
x2+xy+y3=C
The solution of the differential equation dy/dx=x+y using the Euler Method with the initial condition of y(0)=1 and a step size of 0.1 for the first 3 increments.
What is
y(0.1)= 1.1
y(0.2)= 1.22
y(0.3)= 1.362?
Solve for y: xy'+3y=4x^2-3x
y=4x^2/5-3x/4+C/x^3
solve this equation: (dy)/(dx)=x/y
y2=x2+C or y=±√(x2+C)
Solve for y: dy/dx=2x+y/x
y=x(2ln|x|+C)
solve this equation:(3x2+2y)dx+(2x+4y)dy=0
x3+2xy+2y2=C
The term when Zach hall is slacking off
What is Zachin' it?