MTH 108 Section 04. Fall 09 Exam 1, Show all work. Justify procedures and calculations except when they are obvious as, for example, when you integrate both sides of an equation. When doing so, use complete, grammatically correct sentences. No books, notes, calculators. 1. Find the general solution of the equation xy ±-y = 1 in two diﬀerent ways. Check that you obtain the same result. 2. Find the general solution of the equation dy dx = y + 2 x 2 y-x 3. Find a diﬀerential equation whose general solution is given by 3 x 2-xy 3 + y 4 = c where c is any constant. 4. Given the equation d 2 y dt 2 + a 2 y = sin( bt ) , a >0 , b >0 , (a) Find the general solution of the homogeneous equation. (b) Find a particular solution of the forced equation that has form A cos(
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Constant of integration, general solution