Associate the systems with its solution curves: 1. x'=cos(x) y'=sin(x) 2. x'=cos(x) y'=y 3. x'=cos(x) y'=x 4. x'=cos(x-y) y'=sin(x-y) 4 3 > < 1.0 0.5 0.0 -0.5 -1.0 -1.0 -0.5 0 X 0.0 X 2 0.5 1.0

Q: x' = (C )x ´sec X + 0, 1

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Q: Solve: у" + 5у'" — 2y' - 24у — 42е 5t 2y' — 24у 3D 42e — 2, у'(0) — — 6, у'"(0) —D — 30 | | | y(t) =

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Q: Isn't this a Bernulli equation: y'+p(x)y=q(x)y^n   -->     y'=q(x)y^n - p(x)y y'-y/x = x^3 (y-x)^2…

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Q: 8) y'+y=17 sin(2t), y(0) =-1.

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Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

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Q: For the given ODE: ) Convert the higher order ODE to a first order system in matrix form. i) Solve…

A: iwe have, y''+3y'+2y=0 Put x1t=yt x2t=y't ⇒x1'=y'=x2x2'=y''=-3y'-2y       from i…

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Q: Solve the non-homogenous system Sa' = -x – y+ 3/2 ly = 2x – 4y Find lim-00 r(t)

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Q: y as a function of x if '(1) = −2. x²y" +19xy' +81y = x5,

A: Given that the differential equation is                                      To find 'y' as function…