Find the general solution for the differential equation. x dy/dx + 3y = 4x2 – 3x; x>0 y=_______
Solve the exact differential equation (4x*y+sinx)dx+(x4-y)dy=0.
Find the solution of the differential equation dy dx = x y that satisfies the initial condition y(0)=−7. Answer: y(x)=
The differential equation4xy²+6xy+(4x²y+3x²+1)dy/dx=0Has solutions of form F(x, y)=c whereF(x, y)= _______
5. Given the differential equation: dy 1 +-y = 3x2 dx Find (a) (b) the general solution for the differential equation; and (6 marks) the particular solution for the differential equation if the boundary condition is y(1) =2. (2 marks)
Find the solution of the differential equation with the given initial condition. Dy/dx = 2x + sec^2x/2y, y(0) = 5.
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*...
7) Obtain the general solution to the equation. dy-y + 4x + 1 dx X The general solution is y(x) = Ignoring lost solutions, If any. Fill in Box
Differential Equations 3. (20 points) Find the solution to the differential equation y sin(y) dx + x(sin y - ycos y) dy = 0
consider the differential equation dy/dx = -2x/y. find the particular solution y = f(x) to the guven differential equation witht the intial condition f(1)= -1 umowed for this question. D Consider the differential equatio find the particular solution y = f(x) to the given differential equation with the initial condition f(1) = -1 46) = -1 Hy=f2 xdx 17 2 + C = -x +C (b) (9.6) be the region in the first quadrant bounded by the graph of y...