Determine whether or not the following systems have a periodic solution. (a) x' -2° + y*(1 – x) %3D y = 2*(1+y) – y (b) y +x – x? y = 1+y %3D %3D (c) r(4 + 3r sin 0 – p2) 1+ r2 %3D

Q: (а) 8а + 2у + 32 %3D 0 (b) z = sin(x) + cos(y) (1) (c) z = sin 2+x2+y? (d) z = ey II 2. 10 2 0- -5…

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A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

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Q: What is the general solution of (D® + 20Dª + 100D2) y = 0 Oy = C + C2x + (C3 + Csa) cos 10r + (C4 +…

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Q: 3. Classify the stationary points of (a) f(r, y, z) = x² +x*y+y'z+z7-4 (b) /(.x2, X, r)- 20xy +48r,…

A: Given function is fx1,x2,x3,x4=20x2+48x3+6x4+8x1x2-4x12-12x32-x42-4x23           (i) To classify the…

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: The solution of (e® + 2xy²) dx + (2 cos 2y + 2æ?y) dy is given by (A) e + x²y² + cos 2y = c (B) e+…

A: Answer:- The solution of ex+2xy2dx + 2cos 2y + 2x2ydy          —       (1)

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Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

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A: Firstly we define method of undetermined coefficient

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Q: Question 8 Find the solution. (D³ –2D2 -5D +6)y =0; when x =0, y=1, y'= -7, y"= -1 A y = -e-3 + 2e2*…

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Q: (10) y "+10y "+34y '+ 40y

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A: You didn't mention what should I do with the given equations and this problem is posted as calculus.…

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Q: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.

Q: A. Determine Y» using undetermined coefficients: 1. y" + y' + y = 2xe*

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…