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And we wish to solve for y as a function of x . We do this by integrating both sides:

This a quick introduction to Differential Equations. A “Diff EQ” contains derivatives and thus many times involves integration to solve. An example of one is:. And we wish to solve for y as a function of x . We do this by integrating both sides:. Integrate both sides to solve.

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And we wish to solve for y as a function of x . We do this by integrating both sides:

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  1. This a quick introduction to Differential Equations. A “Diff EQ” contains derivatives and thus many times involves integration to solve. An example of one is: And we wish to solve for y as a function of x. We do this by integrating both sides:

  2. Integrate both sides to solve Why isn’t there a constant on the left hand side? There is, or was, it was combined with the one on the left. The above equation is called the “General Solution” of the Diff EQ

  3. Now suppose we have an equation With an initial condition y(2) = 6 We use this to find a particular solution from the general solution: Finding a value for C gives the particular solution

  4. Here is a typical Diff EQ that begins with acceleration and ends with a position function. How high will a ball travel if it leaves your hand 4 feet above the ground and is thrown with an initial velocity of 64 feet per second straight upwards? On Earth, we know the acceleration due to gravity is -32 ft/sec2 This is our starting point.

  5. We will integrate to find the velocity function We have the initial condition v(0) = 64 This will give C = 64

  6. To find position we integrate the velocity function with the initial condition s(0) = 4, the height at which the ball leaves your hand. This gives C = 4 after plugging in t = 0

  7. We have found the position function: If we know how long it takes for the ball to reach the top of its flight, we can find this by plugging in that value of t. We will find this using the velocity function.

  8. At the top of the flight, the ball will stop, then fall back down. To find how long it took to reach the top, solve the velocity function equal to 0 It took 2 seconds to reach the top The maximum height reached is s(2)

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