Question 1 (25 points) 1-1. (15 points) Given the following first order ODE Eq. (Q1-1) (ey + 2x)dx + eydy = 0 (a). (5 po

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Question 1 25 Points 1 1 15 Points Given The Following First Order Ode Eq Q1 1 Ey 2x Dx Eydy 0 A 5 Po 1 (53.63 KiB) Viewed 17 times

Question 1 (25 points) 1-1. (15 points) Given the following first order ODE Eq. (Q1-1) (ey + 2x)dx + eydy = 0 (a). (5 points) A student gives a general solution xey + 2x = c, Sol. (Q1-1) Where c is an arbitrary constant. Verify whether Sol. (Q1-1) is the solution of Eq. (Q1-1) Justify your answer. (b). (10 points) Solve y(x) for the initial condition y(0) = 1. 1-2. (10 points) (a). (7 points) Solve the following Bernoulli equation y'(x) - y(x) = y4(x) Eq. (Q1-2) (b). (3 points) Based on the solution found in 1-2(a), find the limit of y(x) when x → 0.