find the particular solution to the ode GrudeO00.Emil uip ureDoc Sharing Dropbox

Question

find the particular solution to the ode

GrudeO00.Emil uip ureDoc Sharing Dropbox . Journal ach Suppart 2. mco 41 Find the geneai solution for the ful0wing ODE.Y + 2ry = 4x then verify your solution by taking th" appropriate dervstives and subetibuting back into the ariginai Cot.(Points: 3) a. (rco 4) Find the particular salution to the ODE in the preceing problem using the follewing isitiel condits ‘ condition, y(0)--(Part.2) . (rco a) using the method of Runge- Kutta, fInd an asproximate solution to the 00y, that passes through P/3.t), using

Explanation / Answer

(2) dy/dx = 4x - 2xy
dy = 2x(2 - y) dx
dy/(2 - y) = 2x dx
1/(2 - y) dy = 2x dx
-ln|2 - y| = x² + C
ln|2 - y| = -x² - C
e^(ln|2 - y|) = e^(-x² - C)
2 - y = Ae^(-x²), A = e^-C
y = 2 - Ae^(-x²)
(3) y(0) = 9/2
9/2 = 2 - Ae^(-0²),
9/2 = 2 - A(1) => A = 2- (9/2)= -5/2= -2.5

y = f(x) = 2 + 2.5 e^(-x²)

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