Q1: Find the general solution to the ODE:
y'' + 4y' + 13y = 0.
The given ordinary differential equation is
y'' + 4y' + 13y = 0
which is the required general solution of given ordinary differential equation.
Find the general solution of the homogeneous equation (a y" - 4y' + 13y = 0.
For the differential equation y" + 4y' + 13y = 0, a general solution is of the form y = e-2x(C1sin 3x + C2cos 3x), where C1 and C2 are arbitrary constants. Applying the initial conditions y(0) = 4 and y'(0) = 2, find the specific solution. y = _______
(2) (4 marks.) Find the general solution of the ODE e-2x Y"' + 4y + 4y = X > 1. 2
Differential Equations Consider the homogeneous differential equation: y"-4y' +13y = 0. What is a real general solution of the differential equation? y=cje:5X+c2eX y=e2X{ccos 3x+c2sin 3x) y=e=24c1cos 3x+Czsin 3x) y=c1e5x+c2e
Determine the general solution by solving the ODE system 2r+y = 4y
Q5) Find a general solution. Check your answer by substitution. 4y" – 25y = 0 y" + 36y = 0 y" + 6y' + 8.96y = 0) y" + 2k%y' + k4y = 0 Q6) Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2 4y" – 4y' – 3y = 0, y(-2) = e, y'(-2) =...
Consider the ODE below. y' + 4y sec(22) Find the general solution to the associated homogeneous equation. Use ci and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions Vi and U2 produced by the system of equations. Let vi be the function containing a trig function and U2 be the function that does not contain a trig function. You may omit absolute value signs and use...
9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
2. Find the general solution to y(4) -4y" +14y" +44y+25y 0 3. Find the general solution to y" +y-sin r
4. (15 points) Find the general solution of the following second order differential equations. (a) y - 4y + 13y = 0 (b) y' +12y +36y = 0 (c) t’y" + 4ty' - 4y = 0