[i 0 0 Suppose A = 0 1 9 7 -3 0 and b(t) = 0 , then find the solutions of the given system of | sin t XP = AX and (ii) XP equations (i) AX +b(t). dt %3D dt

Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

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Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 2i + 9j – 4k. (a) U X V (b) (c) v x v

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Q: Show that the equation dy + 2k possesses solutions of the form Σ 2 c, e cos (a, x+ E,) cos (w,t +…

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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…

Q: 3r dθ+4θ dr=r2θ3 dr (SOLVE USING NON-EXACT METHOD OR INTEGRABLE COMBINATION)

A: Given differential equation is, 3rdθ+4θdr=r2θ3dr

Q: d) y" + y = sin 2t, y(0) = 2 and y'(0) = 1

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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: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

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Q: Find u x v, v x u, and v x v. u = 4i + 7k v = 6i + 9j - 5k. (a) ux v (b) (c) V x u V X V

A: We have given two vectors u and v and we want to find the cross product of the given vectors in…

Q: 2xy - 10y -x + 5 y - 6 xy + 5y + 2x + 10 -dx +- 0 %3D 2.x + 3

A: Separable Differential Equations: A separable differential equation is an equation that can be…

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

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Q: Find the solution. y'-y = -xy1/2 -ху

A: This is Bernoulli type differential equation.

Q: find all the values of a such that y=xa is a solution of yII-12x-2y=0

A: The objective of the question is to find the values of 'a' for which the function y = x^a is a…

Q: General Solutions (D2+2D+2)y=5cosx+10 sin2x

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Q: Find two solutions to 2y′′+ 5y′+ 2y= 0

A: for the homogeneous system, the auxiliary equation is given by

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: Linear Algebra  2. Find all the values of unknown variables which satisfy the following equation:…

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Q: 24 + 16 = 0 e22-2z-3 = 0 iz = (-i)(-i)

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Q: xy" – y' + xy = 0, t =

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Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: The roots of the characteristic equation of (D2 – D + Dy3 0 are 11 = 2 + 3i and A2 = 2 - 3i.

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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…

Q: 2х + 3 dx Vx + 2 J 3 4 Answer: (x + 2)7 – 2(x + 2)7 + C

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Q: Solve the ifferential equation (D2-2D+2)y=cos9x

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

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Q: Solve for x and y and determine if e 1 f 16x - 2 VDAS 4x+ 8y + 1 |12y-9 f 6.

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Q: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy = 0

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Q: What is the most appropriate substitution equation in order to solve the equation…

A: The given differential equation is -  (x+2y-1)dx+3(x+2y)dy=0 Rewriting the above equation as  -…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.