Unformatted text preview: v ( t ) for any t > 0 (up until the object strikes the ground). Show v ( t ) approaches a limit as t → ∞ . 4. ( Linear Diﬀerential Equations ) Solve the diﬀerential equations in parts (a)–(b) (a) dy dx-2 y x = x 2 , y (1) = 2 (b) x dy dx-4 y = x 5 e x , y (1) = e 5. (a) A Bernoulli diﬀerential equation is of the form dy dx + P ( x ) y = Q ( x ) y n Observe that if n = 0 or n = 1, the Bernoulli equation is linear. For other values of n , show that the substitution u = y 1-n transforms the Bernoulli equation into the linear equation du dx + (1-n ) P ( x ) u = (1-n ) Q ( x ) (b) Use the method in part (a) to solve the diﬀerential equation dy dx + 2 x y = y 3 x 2...
View Full Document
- Fall '08
- Differential Equations, Trigraph, Elementary algebra, Koray Karabina