If y(t) is a solution of the differential equation y"+by'+2y = t?cos(t), then ... (A) ... lim y(t) = ±∞ , if b<0 Neither (A) nor (B). O Both (A) and (B). (B) . lim y(t) = 0 , if b>0 ..

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A: We have to use Linear Approximation.

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A: We have to solve given problem:

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A: Given: RdQdt + QC=E The given equation can be written as dQdt +QC=ER

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A: Here I am attaching image so that you understand each and every step.

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A: Given, y'=ty-5 And f(t) is a solution of the differential equation. The graph of f(t) passes through…

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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Q: For the differential equation (x2 – 16)y" + (x – 4)y' + 2y = 0, the singular %3D points are: O x=4…

A: Let us consider the differential equation y''+P(x) y'+Q(x)y=0 Where P(x) and Q(x) are function of x…

Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

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Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A: Explanation  we have given the voltage change E across the heart satisfies the linear differential…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: Note the following chain rule of differentiation : For a differentiable function y=1f(x)  , y' =…

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Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

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A: Given second order differential equation  3d2ydx2+5y=2y''+1 A second order differential equation…

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A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

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A: We have to solve given problem:

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A: For the solution follow the next steps.

Q: Solve the non-linear Differential Equation y"=-e xy = f(x) by explicitly following these steps:…

A: Use the following formulae, to obtain the solution.

Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: Consider the differential equation dy dx with a particular solution y = f(x) having an initial…

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Q: Solve the Euler-Cauchy differential equation dy -3x + 4y = dx In?x - Inx

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Q: Let y be a solution of the differential equation * + (1+ )y = !, where x > 0 such that y(1) = 1+2.…

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A: Given problem is :

Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). x³y"" + 6x²y" + 4xy' - 4y = 0

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Q: Suppose that the number x(t) (with t in months) of alliga- tors in a swamp satisfies the…

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Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

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Q: 4. Find the differential equation of a family of circles, each having its center on the line y = x…

A: To find the differential equation of a family of circles, each having its center on the line y=x,…

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A: The given differential equation is                                                         1+ln…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

A: Solved below

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A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

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A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…

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A: Start by splitting the variables and integrating each side of the equality:…