No 4. Solve the differential equation dy dx . Solve the initial value problem: y" +...
dy 1.A. Solve the differential equation: = = y2ex dx dy B. Solve the initial value problem: + 2y = 3x2 ; y(0) = 1 dx C.A certain radioactive substance has a half life of 1300 years. Assume an amount yo was initially present. a.Find a formula for the amount of radioactive substance present at any time t. b.In how many years will only 1/10 of the original amount remain?
Solve the differential equation. 7) dy Y-(In x5 7) dx х Solve the initial value problem. 8) e dy + y = cos e; e > 0, y(n) = 1 de 8) Solve the problem. 9) A tank initially contains 120 gal of brine in which 50 lb of salt are dissolved. A brine containing 1 lb/gal of salt runs into the tank at the rate of 10 gal/min. The mixture is kept uniform by stirring and flows out of...
Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x) Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x)
of 3. Solve the differential equation y de + - dx +(2y Inx - 3sin (3y)) dy = 0.
Solve the following initial value problem y(0) = 0 cosx (dy/dx) - ysinx = 3x^2
Solve the following exact differential equation with initial value. (5x + 4y)dx + (4x - 8y3)dy = 0, y(0) = 2
Problem 4. Verify that the differential equation is exact then solve it! (4x + 2y)dx + (2x + 4y)dy = 0 Answer:
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
Solve initial value problem (IVP) dy 2y- х dx V x2 – 16 = 0, y(5) = 2
Problem 5 (25 points) Show that the differential equation (siny -ysinx)dx + (cosx + xcosy - y)dy = 0 is exact, and hence find the general solution. Solve the following. Simplify answers as much as possible. (a) (1+y?)dx -xydy = 0 , y(5) - 2 (b) e(sinx)dy +(e X + 1 cosx)dx = 0