299_pdfsam_math 54 differential equation solutions odd

299_pdfsam_math 54 differential equation solutions odd -...

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Exercises 5.4 6. We see by Definition 1 on page 266 of the text that we must solve the system of equations given by y 2 3 y + 2 = 0 , ( x 1)( y 2) = 0 . By factoring the first equation above, we find that this system becomes ( y 1)( y 2) = 0 , ( x 1)( y 2) = 0 . Thus, we observe that if y = 2 and x is any constant, then the system of differential equations given in this problem will be satisfied. Therefore, one family of critical points is given by the line y = 2. If y = 2, then the system of equations above simplifies to y 1 = 0, and x 1 = 0. Hence, another critical point is the point (1 , 1). 7. Here f ( x, y
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