To solve this problem, I would first write out the homogenous equation allowing me to notice that it is a second order differential equation. To find y1 and y2, I would write out the characteristic equation, solve for r and use those values to find out which case it is so I know what y1 and y2 should be. Next, to find the particular solution, Yp, I would use the variations of parameters method to find u1 and u2 which are mystery functions and use that to construct Yp. Finally, to determine the general solution I would put together Yp plus the solution the homogeneous equation which is c1y1 + c2y2 making y = Yp + c1y1 + c2y2.
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This course is based on the following course(s):
- MAT1375 by Jonas Reitz
- MAT2680 by Jonas Reitz
Recent Comments
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I had a different test version than you. I had test version D and comparing your question #4 to mine I noticed the numbers were exactly the same. For this question I didn’t receive full credit so re-attempting this problem I noticed my work is quite similar to yours. The one difference is how I wrote my work when I solved for yp’ and yp’’ I wrote d/dx (yp) to get yp prime and d/dx (yp’) to get yp double prime. This way of writing using “d/dx” is more familiar for me and allows me to check my work to see if my calculations were done correctly. Your work is well written and very neat. It was also well organized which made it easier for me to follow.