4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0 4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
2. 2. Is y²dx + (2xy + cosy) dy = 0 exact?
Determine whether the equation is exact. If it is, then solve it (2xy + 3)dx + (x²-6) dy=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The equation is exact and an implicit solution in the form F(x,y)=Cis-C, where is an arbitrary constant (Type an expression using x and y as the variables.) OB. The equation is not exact,
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
Consider the equation 2xy (y dx + x dy) = (y dx - xdy) sin - Is the equation exact? If not, find an integrating factor, and solve the equation that is exact with the integrating factor
15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
Solve the initial value problem (2x – y2)dx + (1 – 2xy)dy = 0, y(1) = 5
dy dx Find when x = 3 and = -2, given that x2 + y2 = 35. dt dt dy (Round to two decimal places as needed.)
2. Show that the differential equation below is exact and find the general solution. (2xy + 2 y) dx + (2x+y+2x)dy-0