Solve the following initial-value problems using the integrating factor method. In each case show that your solution satisfies the differential equation. (a) (b) -2x = 3e, x(1) = 3, + 3x=t, x(0) = 1.

Q: use some form of technology to factorthe auxiliary polynomial of the given differential…

A: The given differential equation is yiv+4y'''-3y''-64y'-208y=0 We have to find the general solution…

Q: The differential equation below models the temperature of a 87°C cup of coffee in a 21°C room, where…

A:

Q: Find the general solution of the differential equation y′ = √x y

A:

Q: x(x+y)(dx + dy) = 2 (xdy – ydx). %3D

A:

Q: Find the general solution of the differential equation. y (4) y = 7t+cost. - NOTE: Use C₁, C2, C3,…

A:

Q: Solve the problem. Solve the differential equation model of a population growth: dP 0.5P. dt O P(t)…

A:

Q: Find value of the NEGATIVE root for: a = 4.7 and b = 4.6 and c = -4.1. Give your answer to 3 decimal…

A:

Q: Solve the differential equation x"(t) - 4x(t) = t using the factorization method.

A:

Q: 1. A circle has a general equation 3x² + 3y² - 2x +y-5=0. Convert into standard equation. 2.Find…

A:

Q: Find the general solution of the differential equation. y (4) - y = 8t + cost.

A:

Q: check if the given vectors are linearly independent or not . {(-1, 1, 0), (-1, 0, 1), (1, 1, 1)}.…

A:

Q: Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population…

A:

Q: Find the general solution of the Differential Equation (DE) y6 +y =0.

A:

Q: dy = -y + 2 with the initial value y(0) = -2 dx

A: Explanation of the answer is as follows

Q: Find the general solution of the differential equation. y(4) y = 15t + cost. NOTE: Use c₁, c₂, C3,…

A: We Solve given Differential Equation.

Q: Find

A:

Q: (y+2)dx +y(x+4)dy = 0 ; y(-3) = -1 a. Identify the Differential equation if it is an ODE or PDE. b.…

A:

Q: f(x) = 2x + 1; ¹/f = x² d.x

A: Solution: Given, f(x) = 2x + 1;  dfdx=x2 We have to check whether f(x) = 2x+1 is the solution to the…

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: 2) find the complete solution of the differential equation x dy +Jx²-y*dx = ydt

A: given xdy+x2-y2dx=ydxxdy=(y-x2-y2)dxdydx=(y-x2-y2x)put…

Q: Solve the differential equation dy dx I 36y a. Find an implicit solution and put your answer in the…

A:

Q: Solve the given Differential Equation (4x+y-1)dx+ (x-y-4)dy=0 Solve using the coefficient linear in…

A:

Q: Write down the solution of the differential equation: y+4y +3y 0 if y(0) - 2 and y (0) =3

A:

Q: FOR PART C, can you explain how they got the quadratic equation

A: The growth of a population over time P(t) is modeled by the differential equation .To Find:Explain…

Q: Find the general solution of the differential equation: y' + 2y = 2 sin (3x) Use Uppercase C for the…

A: