y" +6y' + 4y = 10e ; y(0) = 0, y'(0) = -2 Answer: y = et -e-t +e-* 3

Q: dy dt ty 1-2X=65+

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Q: du/dt = (1/ln(t+u))  -1

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Q: Discuss the Error in Differential Approximation?

A: Given: Discuss the Error in Differential Approximation?

Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: 5. 6. Solve fo e-t sint dt. dt. t Solve fe-t. -t sint t

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

Q: Find the differential of each function: (a) y =(x' -3)* (b) y= V1-

A: Solution of this question is

Q: Solve the equation (x+2) Siny dx + X cosydy=1 собуду=0

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Q: Transform the differential equation 4y′+2y=t^(5) y(0)=9 into an algebraic equation by taking…

A: The given differential equation .Using the Laplace transformation to find an algebraic equation and…

Q: 3.2 y" – 2y' + 5 = -8e¬X, y(0) = 2 and y'(0) = 12.

A: Given y" - 2y' + 5 = -8e-x

Q: y = e - 2x %3D sine

A: First, find the auxiliary roots from the given equation. Use yx=c1y1+c2y2 to write complementary…

Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

Q: A ball is dropped from a point 100 m

A: Given, a ball is dropped from a point 100 m above the ground with zero initial velocity.

Q: Find the general solution of the differential equation with the help of lablace transform

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Q: Let TE L(V, W), where V and W are finite-dimensional. Prove that rk(7) rk(7*).

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Q: Consider the differential equation I+y Using isoclines, construct a direction field, maybe even plot…

A: Given: y'=x-yx+y

Q: Q1} Find the differential of ex²

A:

Q: Can you provide 1 example of Differential Operators (4th order 1 Imaginary and 1 Repeated Distinct…

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Q: Retrieve Faraday's law in differential form from E = -VV ot

A: Consider the given equation, E=-∇V-∂A∂t So, it can be written as, E→+∂A→∂t=-∇V As we know that Curl…

Q: Consider this ordinary differential equation (ODE): dy da At the point (-0.5, 1.5), the direction…

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Q: Is the logistic equation a linear differential equation?

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Q: d'a b. = -ka dt? Solve the differential equation and Express the x as a function of trigonometric…

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Q: Gニ +3.94 り(s) = \ y(0)= 3.9

A: According to the given information, it is required to solve t he given differential equation using…

Q: Solve the differential equation 5y" - 5x2y" -10xy' + 100y = 0 . Then evaluate the Legendre…

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Q: Solue the Differential equation by using the method of Laplace Transforms = 3x2 given ylo)=0 and y'…

A: The given differential equation is y"+2y' = 3x2    ----  (1) with initial conditions y(0) = 0, y'(0)…

Q: Find the differential equation of All parabolas whose axis is parallel to the y-axis. Draw at least…

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Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate

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.