Find a general solution to the given equation for t < 0. 5 34 y'(t)- y(t) + y(t) = 0

Q: what is the general Solution to the equation (o²+D)y(x)=x

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Q: Solve the seperable equation for. (dy/dx)=(1+x)/xy12;x>0 Use the following initial condition:…

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Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: Express y = = In(2t), y = 1- t in the form y = f(x) by eliminating the parameter.

A: Given: x = ln(2t) and y=1-t Solving for x in terms of t. x=ln((2t) Take exponential on both sides,…

Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: 13. Solve the exact IVP: (ex + y) dx + y(0) = 1 : (2+x+yey) dy = 0

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Q: Find the general solution of the equation below. Then, find the particular solution which satisfies…

A: To find  The general solution of the given differential equation.

Q: 4. Find the GS of x'(t) = (²4₁) X(t) + (1) et + (9) t -t 1

A: Given that the differential systemX't=241-1Xt+10e-t+01tX't=241-1Xt+e-t0+0tX't=241-1Xt+e-ttThis is in…

Q: Solve the following ODE [y" +9y = (18t) ⋆ d(t — 5) y(0)=0 y'(0)=1

A: L{sin(at)}=a/(s²+a²)L{cos(at)}=s/(s²+a²)L{tn}=(n!)/sn+1 , if n is positive integer .The convolution…

Q: 1. Solve for y: (a) x² + y = 20 (b) 3y - t = t³-y (c) xy + zx = y (d) 2ye - e In x = 3x4

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Q: 9. At time t= 0 a particle is at the origin. It then begins moving along the positive x- axis so…

A: For part (a):

Q: is equal to 1)

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Q: (a) Find the derivative. y In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - 5 y = In x3 dy…

A: a) First we shall find the derivative of y=ln4x-5-3lnx Now,…

Q: Solve the initial value problem for y as a function of x. (x² + 25) dy %3D 29, у(5) %3D 0 dx

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Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

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Q: 2. The acceleration e²t - 25 of a particle at time t > 0 is given by a(t) + 2. Given that the…

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Q: The solution is the fünction y=x' F+= ex* -x? H.W: Solve the following equations 1- x2+3y = x2 2-…

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Q: A particle moves along the x-axis, its position at time t seconds given by s(t) = et - 2t meters.…

A: The objective is to solve the above question.

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

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Q: dy Solve dx = xy using Runge-Kutta method for x = 0-2 given that v (0) I taking %3D h = 0-2.

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Q: Qll Solve the Ivp y'= t = y(o)=0 ز

A: Given:y'=t ;y(0)=0

Q: Find the derivative of the following functions. 2. y=e* sec sec x 1. xy=(x-y)+1

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

Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

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Q: Use p(x) = In(x² + x + 7) to answer the questions below. (a) Find p'(x) = (b) Find the equation of…

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Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…