Consider the following initial value problem: dy = sin(x - y) dx, y(0) 1. Write the...
Solve the initial value problem. (6+av+x]dx + (8yx? + sin y) dy = 0, y(t) == The solution is (Type an equation using x and y as the variables. Type an implicit solution. Type an exact answer in terms of t.)
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...
Solve the initial value problem 2yy'+3=y2+3x with y(0)=4a. To solve this, we should use the substitution u=With this substitution,y=y'=uEnter derivatives using prime notation (e.g., you would enter y' for dy/dx ).b. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'c. The solution to the original initial value problem is described by the following equation in x, y.
Solve the initial value problem. dy = x(y-5), y(0) = 7 dx The solution is (Type an implicit solution. Type an equation using x and y as the variables.)
Problem 3: Find a solution to the IVP dy dy + dc2 + y = 0, y(0) = y'(0) = 1. dx Problem 4: Suppose you are given the differential equation ay" +by' + cy = 9(2) where a, b, and c are constants. For each of the following choices of g(x), write down the form for the particular solution Yp that you would use: (a) g(x) = 205 (b) g(x) = x²e32 (c) g(x) = xº cos(x) (d) g(x)...
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
Consider the initial value problem x^2 dy/dx = y - xy, y(-1) = 1 Use the Existence and Uniqueness theorem to determine if solutions will exist and be unique. Then solve the initial value problem to obtain an analytic solution.
Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x) Solve the initial value problem dy dx+2y-4e0y(O)2 The solution is y(x)
Solve the initial value problem. Vy dx + (x - 7)dy = 0, y(8) = 49 The solution is a (Type an implicit solution. Type an equation using x and y as the variables.)
Solve the initial value problem. y dx+(x-7)dy 0, y(8)= 25 The solution is (Type an implicit solution. Type an equation using x and y as the variables.)