hw3.01 - a Since this is a linear second order equation...

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Engr 5A F.Brewer Homework #3 Due Wed at beginning of class. Reading: Handout (especially “more techniques”) Ref: Ma 5a Text 1. Find general solutions for the following linear differential equations: Hint: if you can’t make the equation into a known form, try to substitute u = f(x) for some f(x) to make a simpler problem. a. b. c. 2. Find a nonzero solution of the equation: by inspection, then use the theorem from last homework to find a solution of: such that y=0 and y’=4 when x=0. Hint: it is easy to find the first solution -- then use it to make a first order equation for the other soluion... 3. Consider the resonant RLC circuit from the notes subjected to a sinusoidal ‘drive’ as follows:
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Unformatted text preview: a. Since this is a linear second order equation, find the general solution by adding a particular so-lution to the solutions from the notes. b. Plot v(t) for the case R=0.1, L=0.01, C= 0.01, and alpha is 1000, for t=0 to 0.03 sec, given v(0)=0, v’(0) = 100 V/sec. (You might want to use a computer for this. ...) y ′′′ 2 y ″ – 3 y ′ – = y ″ y ′ – x 2 = x 2 y ′ y 2 + xyy ′ = y ″ 4 y ′ – x 2 y ′ 4 y – ( 29 + = y ″ 4 y ′ – x 2 y ′ 4 y – ( 29 + 2 xe x 3 3----– = v '' R L---v ' 1 LC-------v + + α t ( 29 sin =...
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