[1 0 Го then find the solutions of the given Q2. a) SupposeA='0 o 'and b(f) 1 | 19 7 31 sint] - dX dX system of equations (i) and (ii) = AX + b(t). AX wwww wwwww dt dt

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Q: The general solution of y" - 4y + 8y = 0 is: Select one: а. ce?"cos2t + cze?'sin2t b. -6t + Cze2t C.…

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Q: Question 10 152 0 0 1 Describe all solutions of Ax = 0 in parametric vector form, where A = 0 0 0 0…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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Q: Q4) Solve the following nonlinear system : cos(3x) + cos(y) = 0 cos (5x) + sin(y) = 0 where %3D %3D

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A: A differential equation of the form Mdx+Ndy=0 is said to be exact differential equation if it…

Q: (D3 - 5D² + 8D-4)y=e2x, Find Y = Yc - Yp a. 2x cé + Cẻ +C xe O C. -2x O b. 2x 2x °°€₁p² + €₂²³ +…

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Q: Obtain the general solution unless otherwise instructed NONHOMOGENEOUS EQUATIONS: UNDETERMINED…

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Q: • Solve the equation using homogenous equation (5v-u)du + (3v - 7u)dv = 0 a.)(3v +u)² = c(v - u)…

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Q: The particular solution for the equation: (d2y/du2) + (dy/du) + y = e3u yp(u) = ? a) (1/11)e3u…

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Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: 1 0 5) Solve the equation x'=| 2 1 -2 ). x X 13 2 1

A: The given problem is to find the solution for the given matrix differential equation.

Q: Use D-operator methods to solve (1) (0²+16)y= tsint Cii) (D²+D+5)y =t coszt %3D

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A: The given differential equation is y''+2y'+y=2e-x1-xsin 3xy''+2y'+y=2e-x-2xe-xsin 3xHere the…

Q: The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. xsin (3x) + y + 5y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: solve: [x X2 X3 Б 1 0 002-20 X1 0-1/2 0 140x₂ 0 00 01 0-1] LxS) ха 0 -12 + +2] 3et+ - 1/4 0 0 with…

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

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A: To solve the given differential equation.

Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: ) (2ху — tanу)dx + (x* — хsec*y)dy 3D 0

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: 15- 2° + V16 – 10 + 5(2) = |

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Q: 9) Solve the equations by Cramer's rule: 2x-y + 3z=-3 3x+3y-z=() -x-y+z=-4

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Q: 14. Solve the following simultaneous equations. (a) 3x + y = 5 (b) 7x + 2y = 11 7p-q=8 3p +5q = -2

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.