For the Initial Value Problem given below:

Q: 24- ex +12x²-6,yc0)=2, yo)=3

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Q: Solve the initial value problems.

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Q: t(t-1)dx t(t-1) = x(x + 1), x(2) = 2 dt

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Q: In the absence of predators the population of mosquitoes in a certain area would increase at a rate…

A: Given initial population of mosquitos is 200000 and the get triple every week, Flock birds eats…

Q: (a) For the the following initial value problem: 60 y(0) = -3 24 i. Find the solution. ii. The…

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Q: (iii) y" – y = (x+1)², y(0) = 1, y'(0) = 1. %3D %3D

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Q: Exercise 3. Solve the following initial value problems. (1) (cos t)y' + (sin t)y = 1, and y(0) = 5;…

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Q: y(x + y+ 1)dæ = –(x+ 2y)dy,

A: To solve the below initial value problem. yx+y+1dx=−x+2ydy,   y0=1

Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

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Q: Given y₁ (x):=x sin x as one of the linearly independent solutions of the equation x²y" + xy + (x² −…

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Q: y" – 2y' + 2y = 0, y(0) = -2, y'(0) = 1 %3D

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Q: Use the method of Laplace transforms to solve the given initial value problem Here, x' and y' denote…

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Q: 2y" - 5y' + 3y = 0, y(0) = 3, y'(0) = -4

A: Given equation is 2y''-5y'+3y=0   Also given y(0)=3 and y'(0)=-4

Q: (In a + 12x y cos a + x*y cos x)dx + (8xy cos x + 2x"y sin x)dy = 0, 4 2 y(T) = 1/27 b. y da - a(a?…

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Q: y" + 4y' + 5y = 8(t) + 8(t - 2π) y(0) = 0 y'(0) = 2

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Q: 3. As in the previous problem, consider the initial value problem dy dt = 2y √(1- 100), with y(0) =…

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Q: (v) y" – y = sech(x), y(0) = 0, y'(0) = 0. NOTE: sech(x) is the hyperbolic secant of x. In (v), it…

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Q: : Ebobl Qf solve the initiat Valu problem %3esince-2) y(an2) =a

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Q: a.) 2y + y = 0, b.) y" - 10y' + 9y = 5t, y(0) = -3 y(0) = -1 and y' (0) = 2

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Q: Consider the initial value problem y +y=1- (0) = 4 y(0) = yo-

A: We have to solve given initial value problem:

Q: Let A = 1.1 0.3 -0.1 0.7 Is matrix A invertible? How do you know?

A: 4 QUESTION ANSWEr |A|=ad -bc  DetA not equal to zero so matrix inversion exists  Cofactor of A=…

Q: (4xy + 3x²) dx + (2y + 2x²) = 0, y(0) = -2

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