G5097 - Differential Equations - Chapter 2

What method of integration do you use for each form of equation?

?
x'(t) = h(t)g(x)
Separation Of Variables
1 of 6
x'(t) = q(at+bx+c) with constants a,b,c ϵ R such that b≠0
Transformation
2 of 6
If x'(t) is Homogeneous
Homogeneous Transformation
3 of 6
If x'(t) = -(g(t,x))/(h(t,x)) with (∂g(t,x)/∂x) = (∂h(t,x)/∂t)
Exact Equation
4 of 6
If x'(t) = -(g(t,x))/(h(t,x)) with (∂g(t,x)/∂x) ≠ (∂h(t,x)/∂t) but it is possible to find a function m(t,x) such that (∂mg(t,x)/∂x) = (∂mh(t,x)/∂t)
Integrating Factor
5 of 6
x'(t) = a(t)x+b(t)
Linear Equation
6 of 6

Other cards in this set

Card 2

Front

x'(t) = q(at+bx+c) with constants a,b,c ϵ R such that b≠0

Back

Transformation

Card 3

Front

If x'(t) is Homogeneous

Back

Preview of the front of card 3

Card 4

Front

If x'(t) = -(g(t,x))/(h(t,x)) with (∂g(t,x)/∂x) = (∂h(t,x)/∂t)

Back

Preview of the front of card 4

Card 5

Front

If x'(t) = -(g(t,x))/(h(t,x)) with (∂g(t,x)/∂x) ≠ (∂h(t,x)/∂t) but it is possible to find a function m(t,x) such that (∂mg(t,x)/∂x) = (∂mh(t,x)/∂t)

Back

Preview of the front of card 5
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