15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
Find an integrating factor for (2xy^2)dx + (2x^2y+x^2y^2)dy = 0
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
solve the following differential equations (e* + 2y)dx + (2x – sin y)dy = 0 xy' + y = y? (6xy + cos2x)dx +(9x?y? +e")dy = 0 +2ye * )dx = (w*e * -2rcos x) di
(d) The line integral [(x+y?)dx + (x2 + 2xy)dy, where the positively oriented curve C is the boundary of the region in the first quadrant determined by the graphs of x=0, y=x2 and y=1, can be converted to A 2xdydx 0 0 BJ 2 xdxdy 0 0 С -2x)dyda 00 D none of the above (e) Consider finding the maximum and minimum values of the function f(x, y) = x + y2 - 4x + 4y subject to the constraint...
Solve the initial value problem (2x – y2)dx + (1 – 2xy)dy = 0, y(1) = 5
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
Please show steps. Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Euler's method is most nearly 5.333 1.010 -0.499 17.822 Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Runge-Kutta 4^th order method is most nearly 5.333 1.010 -0.499...
show the ivp is an exact de and then solve (2xy - 9x^2)dx + (2y + x^2 + 1)dy = 0, y(0) = -3
(1 - -*)dx + (2xy + + + or? y? 2-)dy = 0 y J