Calculus 2 Lecture 8.1: Solving First Order Differential Equations By Separation of Variables

Calculus 2 Lecture 8.1: Solving First Order Differential Equations By Separation of Variables

[darthboganis]

What is a differential equation? 1:00
Example of a 1st ODE 3:00
Functions in terms of x and y 5:00
Example 8:00
More on the differential Equation 14:30
The initial condition 17:00
Example 20:00
The initial value at zero gives the constant C 23:00
Separable differential equation 26:00
What is Separable and what isn't? 30:00
Example 35:00
Example 40:00
Example 56:00 A separable equation. A product (i.e. multiplication) of x and y >> separate them
1:01:30 Writing the C constant
Initial value problem 1:09:00
1:13:00 U-Sub won't work, because the squared term isn't in denominator. Can you split the fractions?
1:15:00 using different subscripts for constants like c1 and c2 is really just making your life easier.
> It works because they're essentially still constant. There are no unknown variables involved.
The initial value gives a specific solution because it allows us to find the constant C, and the general solution is just a family of curves anyways
Natural Growth and Decay 1:18:30-1:44:00
Example 1:44:00 proportionality, solve for e^k
Decay 2:02:00
Law of Cooling 2:18:00
> the differential equation 2:26:30
Solve the differential 2:30:00

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[uhrrtax]

OMG you have just saved my life. Studying for and engi. degree and my proff is so hopeless it is unbelivable and the thing is if i dont get it i fail not only this but also another 15 engi. subjects as everything prety much is based on differential equations.
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[ronnies.]

"You're the teacher. You tell me."
I am sure you will make it far in your career with that attitude, young lady.
Great lectures by the way, Professor Leonard.