Some Differential equation problems

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To find the fundamental set of solutions for the differential equation y'' + y' - 2y = 0 with the initial point t0 = 0, assume a solution of the form y(t) = Ce^{\lambda t} and substitute it into the equation to determine λ. For the spring problem, the setup involves understanding the relationship between force, mass, and damping, with the spring stretched 10 cm by a force of 3 N and a 2 kg mass attached to a damper exerting 3 N at 5 m/sec. To find y, consider the forces acting on the mass and apply Newton's second law. A few hints on the setup can guide the approach without providing complete solutions.
seang
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Hey all, I'm reviewing for an exam and I'm in need of a bump on the following issues:

1.) Find the fundamental set of solutions for the given differential equation and initial point.

y'' + y' - 2y = 0 tsub0 = 0

2.)A spring is stretched 10cm by a force of 3 N. A Mass of 2kg is hung from the spring and attached to a damper which exerts 3 N when the velocity = 5m/sec. There's more but I just need a little help setting it up. I don't understand how to find y (as in yu'(t)). Unless its just 3/5.

Just a few hints would suffice, I'm not asking you to solve these.

Thanks, Sean
 
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for a) you have to assume that the solution looks like y(t) = Ce^{\lambda t} where lambda is to be determined. Substitute this into your expression and you can find your lambda. Also use your initial condiotion to find C.
 

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