ENGR 213 Midterm: ENGR 213 Midterm 2018 Fall
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Name and surname: id: (4 marks) solve the following initial value problem for the first order differential equation dy dx. When x 1, y y c(1 x ). 3 dx c ln y ln(1 x ) c ln y. 3 (1 x ) particular solution. y: (4 marks) solve the following differential equation of the first order. , is the integrating factor. d dx d dx. Created by reinaldo rodriguez: (4 marks) solve the differential equation. N x and the equation is exact. (x,y)= (4x x. 3x g (y) n(x, y) 3x 2y 1 g (y) 2 y c: (4 marks) solve (x + y ) dx 3. We use the substitution y=vx, dy=vdx + xdv, 1 mark: the variables are separable. x (1 v ) dx 3v (vdx xdv) 2 x (1 v ) 3v dx 3v x dv. 3 ln(1 2 v ) lnc, 2ln x.
