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31_pdfsam_math 54 differential equation solutions odd

31_pdfsam_math 54 differential equation solutions odd -...

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CHAPTER 2: First Order Differential Equations EXERCISES 2.2: Separable Equations, page 46 1. This equation is separable because we can separate variables by multiplying both sides by dx and dividing by 2 y 3 + y + 4. 3. This equation is separable because dy dx = ye x + y x 2 + 2 = e x x 2 + 2 ye y = g ( x ) p ( y ) . 5. Writing the equation in the form ds dt = s + 1 st s 2 , we see that the right-hand side cannot be represented in the form g ( t ) p ( s ). Therefore, the equation is not separable. 7. Multiplying both sides of the equation by y 2 dx and integrating yields y 2 dy = (1 x 2 ) dx
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