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# m238sum08t1 - name Mathematics 238 first test Monday July 7...

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name : Mathematics 238 first test Monday, July 7, 2008 please show your work to get full credit for each problem 1 . Is y = e 4 x a solution to the differential equation y - 5 y + 4 y = 0 ? 2 . Is y = x 0 cos t 2 dt a solution of the initial value problem dy dx = cos x 2 and y (0) = 0 ? 3 . Given the differential equation dy dx = ( x 2 sec 3 x ) y ( a ) Is the equation separable? ( b ) Is the equation linear? ( c ) Is the equation exact? 4 . Given the differential equation 3 x 2 y 2 + 2 x 3 y + 12 y 2 dy dx = 0 ( a ) Is the equation separable? ( b ) Is the equation linear? ( c ) Is the equation exact? 5 . Solve the initial value problem dy dx = y 3 (2 x - 5) and y (0) = 3 6 and state the solution’s domain. 6 . Solve the initial value problem dy dx +3 y = 6 x and y (0) = 2 . 7 . Solve the differential equation x dy dx - 2 y = x 3 sin 4 x. 8 . Solve the initial value problem - 2 x - 3 y 3 + 1 x dx + 3 x - 2 y 2 + 2 e 2 y dy = 0 and y (1) = 0 . 9 . Solve the differential equation dy dx +4 y = 2 e - 2 x y using the substitution w = y

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page two 10 . Sketch the direction field & representative isoclines for dy dx = 2+ x y 11 . Suppose that dP dt = f ( P ) where f is sketched below ( a ) What are the equilibrium (or constant) solutions? ( b ) Sketch a phase line for
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m238sum08t1 - name Mathematics 238 first test Monday July 7...

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