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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

Differential Equations
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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.
nope in physics..it is also about laplace.
can you help me?

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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!
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.
is u(t) the unit step function?

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