O2: 16 Marks] Find the general solution of the differential equation (sin x)y" +(cos x)y' cos x b...
(c) (i) Find the general solution of the following partial differential equation y, = 2y sin x + e-x Whatische solution when the initial conditions are v(0,y)--y, and (ii) y(x, 0) = cos x ? (10 Marks)
find a general solution to the differential equation y’=2 cos (x)- tan(x)* y
Solve i. and ii. Given the ordinary differential equation: cos(x)y' = sin(x)y + 1 Find the general solution of the given differential equation. ii. Solve the ordinary differential equation: ay' + by = a cos(wx) + Bsen(wx) Where: a, b, a,ß and w are nonzero real constants.
Find a differential equation such that y=e 2* (c, cos 4x+cz sin 4x) is the general solution of the equation.
a. Find a particular solution to the nonhomogeneous differential equation y" + 4y = cos(2x) + sin(2x) b. Find the most general solution to the associated homogeneous differential equation. Use cand in your answer to denote arbitrary constants. c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 8 and y'(0) = 4
differential lesson Question 2: (40 marks) Find the general solution of the differential equation y" - 3y' – 4y = Sin(t) by using the method of undetermined coefficients.
3. (20 points) Find the solution to the differential equation y sin(y) dx + x(sin y - y cos y) dy = 0
Find the general solution of the given differential equation. x y - y = x2 sin(x) y(x) = (No Response) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (No Response) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) (No Response)
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general solution to the homogeneous differential equation y 00 + 9y = 0 (a) In each case below, write down your “guess” for the form of the particular solution to the differential equation. y 00 + 9y = f(x) Question 6. (Total marks: 14) You are given that y = cos(3x) + sin(3.c) is the general solution to the homogeneous differential equation y" +9y = 0 (a) In...
Differential Equations Find the general solution of the differential equation y" + wäy = cos(wt), W2 + ಎಕಿ.