about y' = x-y, y(0) = 0,
(1) find solution
(2) use direction field draw approximation solution on xy plane and compare with the result (1)
about y' = x-y, y(0) = 0, (1) find solution (2) use direction field draw approximation...
9. Use the method of Frobenius to find a solution of 0. about the singular point x xy "+ (1 + x)y' 0. y 16x n 0 9. Use the method of Frobenius to find a solution of 0. about the singular point x xy "+ (1 + x)y' 0. y 16x n 0
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β. 3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
Find the indicated coefficients of the power series solution about x=0 of the differential equation. (x^2+1)y''-xy'+y=0, y(0)=3, y'(0)=-6 (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9) (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9)
( xy 7. CHALLENGE: fxy(x, y) = 0< < 2, 0 <y <1 otherwise 0 Find P(X+Y < 1) HINT: consider the region of the XY plane where the inequality is true.
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) = 1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS PROVIDED IN THE PICTURES a. Use a Euler approximation with a step size of 0.25 to approximate y(2). b. Use a Runge-Kutta approximation with a step size of 0.25 to approximate y(2). c. Graph both approximation functions in the same window as a slope field for the differential equation. d. Find a formula for the actual solution (not...
Consider the solution to the IVP y' - xy = x; y(0) = 2 Find y' (0) Consider the solution to the IVP y' - xy = t; y(0) = 2 Find y" (0)
Find the general solution around x=0 for (x^2-x)y’’-xy’+y=0
0 t t 0, 1 Question 3 (25 points). Consider the differential equation y' T(xy), where T(t)= 0 -1 t0. (a). Draw the direction field for this DE. (You need only draw 25 line segments in the grid provided.) (b). Verify that y 0 is a solution on the interval (-oo, oo). (c). Explain why y = |x|+1 is not a solution on the interval (-1,1). (d). Explain why y = |z - 4| is not a solution on the...
tel length of wire carrying ? current in the x-axis direction, It forms at any point ? (?, ?) in the xy-plane. find the magnitude and direction of the magnetic field. You get from the result, the magnetic field expressions at points ? (0, ?) and ? (?, ?) Found it. P(x,y) 3. +x-ekseni yönünde 1 akımı taşıyan L uzunluğundaki telin, y xy-düzlemindeki herhangi bir P(x,y) noktasında oluşturduğu manyetik alanın büyüklüğünü ve yönünü bulunuz. Elde ettiğiniz sonuçtan, P(0,y) ve P(L,...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...