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# ODE1 - MAP2302 Test 1(2 pts 1 The auxiliary equation for...

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MAP2302 Test 1 (2 pts) 1. The auxiliary equation for the ODE y 00 + 2 y 0 + 3 y = 0 is given by: (2 pts) 2. In order to solve the equation y 0 + (sin x ) y = ( x 2 + tan x ) y - 3 , one should begin with the substitution v = ? (2 pts) 3. Given ( kye 3 x + tan y + e 3 y ) dy + (5 y 2 e 3 x + sin x ) dx = 0 , what should be the value of the constant k so that the equation is exact? (2 pts) 4. For the equation x 2 y 0 + 3 xy = sin x, x > 0 , the integrating factor is given by: (2 pts) 5. The general solution to the ODE y 00 + 7 y = 0 is given by:

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(2 pts) 6. After the substitution v = y/x, the equation y 0 = y/x + x 2 /y 2 can be rearranged and written as v 0 = ? (2 pts) 7. If y = Ke t / ( Ke t - 1) is a solution to the equation y 0 = - y 2 + y, y (2) = 3 , the value of K is ? (2 pts) 8. For the ODE y 0 = ( - x 2 + 4) / ( y - 7) , the equation of the isocline for which the slope of the solution curves is equal to - 3 is given by y = ? (2 pts) 9. For the equation (sin
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ODE1 - MAP2302 Test 1(2 pts 1 The auxiliary equation for...

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