[H] Consider the differential equation dx 1+x2 (H.1) Find the general solution of the above differential...
d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the form F(x)GK, in which the coefficient of x2 is 84. Answer: =K e. Find the particular solution of the differential equation (4 +x2)으-2V 16-r, such that y-t as x →-2. dx Simplify your answer as much as possible. Answer: y= d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the...
Consider the following differential equation. (x2 − 4) dy dx + 4y = (x + 2)2 Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form. 5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form.
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...
(1 point) In this problem we consider an equation in differential form M dx + N dy = 0. (4x4 + y) dx + (x - y)dy = 0 Find My = Nx = If the problem is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C, give implicit general solutions to the differential equation. If the equation is not exact,...
(1 point) In this problem we consider an equation in differential form M dx + N dy=0. (6x + 6y)dx – (6x + 4y)dy = 0 Find My = N = If the problem is exact find a function F(x,y) whose differential, F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C, give implicit general solutions to the differential equation If the equation is not exact, enter NE otherwise find F(x,y)...
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
Please help (1 point) In this problem we consider an equation in differential form M dx + N dy-0 (- (xy' +y)) dx + (- (x2y + x))dy 0 Find If the problem is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x,...
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
2. (10 pts. Consider the differential equation dy y sin . dr (a) Find the general solution of this equation by the method of your choice. Write the solution in explicit form. (b) Find the solution which satisfies the initial condition un 3