IB`NOT`ez Posted August 3, 2017 Report Share Posted August 3, 2017 (edited) Have had some trouble solving these questions, would appreciate any assistance or suggestions on how to approach the questions. I've tried the substitution y=vx and got to a stage where I am unable to integrate 1/f(y) and then have no idea how to further proceed (for question 7). Question 8 I just have no idea how to approach. Edited August 3, 2017 by IB`NOT`ez Reply Link to post Share on other sites More sharing options...
kw0573 Posted August 3, 2017 Report Share Posted August 3, 2017 (edited) 7 a) To solve any separable differential equation, get expressions of one variable on the same side and integrate: . However the target equation is a definite integral so we need to know the bounds of integration. Because (x, v) = (1, k), (e, 2) are part of the solution, then the bounds are [k, 2] for v, and [1, e] for x. So simplify to get 1 on right hand side. This works by a change of variables (u-substitution) of f(v) = x and {v = 2 <=> x= e, v = k <=> x = 1}. Alternatively, suppose there is y = 1 / f(v) = 1/ x and you are finding the area under the curve 2 different ways. I believe it was a typo and this should be sufficient to answer the problem. However, with constant k defined and function f restrained, and replace with any continuous variable it still hold correct. Regardless of v or y, no assumption of y = vx is necessary for this step. 7 b) i) Assume v = y / x I am trying to get the equation in form of 7a! Finally, at x = e, v = 2 and this is 7a. Here I say that it was a typo because we have f(v), not f(y). 7 b) ii) Calculator 8. Start with Edited August 4, 2017 by kw0573 1 Reply Link to post Share on other sites More sharing options...
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