MAT 2150 Midterm: MAT2150 Wayne State Exam1

• School: Wayne State University
• Department: Mathematics
• Course: MAT 2150
• Professor: All

Document Summary

[15pts] indicate the linearity of the following di erential equations. (i) (ii) (iii) y x dy dx d2y dx2 + 9y = x3, d2y dx2 + y3 = 0. [30 points] solve the following initial value problems. (i) dv dx. = x3(1 + v), v(0) = 3 (ii) dy dx. + 3y e x = 0, y(0) = 1. B (b) transform b into row-echelon form and nd the rank of b(show all the steps). [15pts] solve the system (show all the steps, using row-echelon form ) F (x, y) = (3x3y + cos x)dx + g(y) = x3y + sin x + g(y). Therefore, g (y) = 0 and g(y) is a constant, and the solution is x3y + sin x = c. 1. 2) the equation can be written as y + 3 x y = cos x x3 . p(x) =