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- anonymous

differential equation using classical method. assume zero condition.
anybody can give exact solution?
1.) d^2x/dt^2 + 8 dx/dt+ 25x = 10 u(t)
2.)d^2x/dt^2 + 2 dx/dt+ x = 5e−2t + t
3.)d^2x/dt^2 + 4x = t2

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- anonymous

- jamiebookeater

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- anonymous

These are similar to differential equations in physics with acceleration (d2y/dt^2) and a resistance term (dy/dt). start with y =A exp(kt) and see what you get.

- anonymous

nope in physics..it is also about laplace.

- anonymous

can you help me?

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- anonymous

I was never good at Laplace transforms. Often they are listed in books such as STANDARD MATHEMATICAL TABLES. My recollection is that you use the transform to convert the diff eqn into a polynomial, solve it to some degree, then use the inverse transform to get the answer. Did it decades ago, and not well!

- tkhunny

The "Classical" method is NOT Laplace.
Find the Characteristic Equation and solve for the homogeneous solution.
Add the particular solution.
Then you have a lot of algebra in your future.

- UnkleRhaukus

is u(t) the unit step function?

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