3. a) Show that the differential equation (3x’y + e)dx + (x3 + xey - 2y)dy...
In this problem we consider an equation in differential form M dx + N dy = 0. (4x4 + 2y) dx +(- (2x + y2))dy = 0 Find My Nx = = If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) solutions to the differential equation. C, give implicit general If the equation is not exact, enter NE otherwise find...
Determine whether the equation is exact. If it is, then solve it (3x2y+8)dx+ (x3-8)dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A The equation is exact and an implicit solution in the form F(x.y) = C is _______ = C, where C is an arbitrary constant. B. The equation is not exact.
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...
Determine whether the equation is exact. If it is, then solve it. (3x²y+9) dx + (x3 - 6) dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = A. The equation is exact and an implicit solution in the form F(x,y) = C is _______ = C, where is an arbitrary constant.(Type an expression using x and y as the variables.) B. The equation is not exact.
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
Q4/ Solve the following ordinary differential equation: (ex+y + y ey) dx + (xey - 1 )dy = 0
Solve the differential equation. Do not solve explicity for y. (3x2y + ey) dx + + (x3 + xey – 2) dy = 0
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
Problem 4. Verify that the differential equation is exact then solve it! (4x + 2y)dx + (2x + 4y)dy = 0 Answer:
Solve the equation (2x)dx + (2y - 4x2y-1)dy = 0 An implicit solution in the form F(x,y)=C is _______ =C, where is an arbitrary constant, and _______ by multiplying by the integrating factor.