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full workings preferred thanks x² + * Full workings requined. For x 20 consider the ordinary...
x² + * Full workings requined. For x 20 consider the ordinary differential equation de 2x²+4² - xy 1) find the solution of this differential equation that satisfies the condition that y=2 have the answer in the implicit fam G(x,y)=0. for some function a which you can find. x=2
Show all of the details of your work Consider the ordinary differential equation (x2 + 1) y' + 4xy = 4x a. Find the general. How many solutions does the equation have? b. Determine the that satisfies the initial condition y(0)=5
Find the function y=y(x) (for x>0) which satisfies the separable differential equation dy/dx = (4+17x)/(xy^2). ;x>0 with the initial condition: y(1)=2
(1 point) Consider the ordinary differential equation d2G 05 - G = 8(x – xo) on - < x < 0 dr2 where 8 is the delta function. Find the continuous solution G = G(x) such that limz+- G(x) = 0 and limz-40 G(x) = 0. The function u = G(x) is given by G= G for – 0 < x < XO, G = for Xo < x < 0. In your answers, type coas x0.
Write a Maple program to solve analytically the ordinary differential equation dy dt = y 2 + 1 with initial condition y(0) = 0. What solution is found? Verify (on paper) that the solution found satisfies the differential equation and initial condition.
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...
20 p. #3 Find the solution to the differential equation ry2 – xy? x + xy4 satisfying the initial condition y(1) = -2
PLEASE SOLVE NUMBER 3 AND SHOW ALL WORK 1.Find the particular implci solution to the difterential equatiothat satisfies the condition 1. Find the particular implicit solution to the differential equation dx y y(7)- v5. Sketch a graph of your solution. 2. Write and solve the differential equation the models the verbal statement. Simplify the explicit solution. Temperature of the body and the constant temperature of its surrounding medium M." of a body is directly proportional to the difference in the...
Need help with b) In this problem we will examine the Green's function method for ordinary DE's in a somewhat more general way than presented in the lectures - although you can follow the logic in the lecture notes closely when doing a) and b). Consider the differential equation with specified boundary conditions (a) y(b)-0 We assume that two linearly independent solutions, yı() and y2(x), of the homogeneous equation are known, and that y(a)y2(b) 0 a) Show that the Green's...
0 A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot. Find the work required to pump oil out through a hole in the top of the tank. ② For the differential equation xy-3y=0 verify that y= Cx² is a solution, and find the particular solution determined by the initial condition y=2 when X=-3. find @ Given the initial condition y(0)=1, particular solution of the equation xy dx + e* (y²-1)...