Verify that the solution x= (A+ Br)e™"/2m 50 Dampedi satisfies the equation mž + r* + sx = 0 when P/Am² = s/m

Q: Find '(t), given r(t) = (-4e-²t, 4t² + 3, 3 sin(−3t)). r' (t) =

A: Given vector is as follows

Q: Suppose that fx cos(x²)dx = G(x) + C = F(x). Determine the constant of integration C if F(0) = 2. 0…

A: Given Integral  ∫xcos( x2 )dx∫xcos( x2 )dx = G( x ) + C Given condition F( 0 ) = 2

Q: Given the IVP dx/dt = 1.71(x) at x(0) = 0 Find x(1)=?

A: Given- dxdt=1.71x and x0=0. To Find- The value of x1.

Q: what is the Solution ofequation とdx +(2Xlogk - メy)dyニ。

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Q: e 3x dx ex-1 X .

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Q: Find what m equals given tyll-3kyloMyo the differential equation

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Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Z1 = 4- j4 Z2 = 4 + j3 %3D 1.Evaluate: log(cos(Z1)) 2.Evaluate: tan(Z2) 3. Find all solutions of e^z…

A: Note: Since we are can solve at most three subparts in a question, we have solved the first three…

Q: x³y"+xy'+4y = cos (2 In x)

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Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Solve dN dt = (1¹ 1+ cos(2nt) N where t ≤0 and N(0) = No.

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Q: Solve (t² + 4) da = (x² + 16), using separation of variables, given the inital condition x(0) = 4. x…

A: To solve the following initial value problem by using separation of variables.

Q: Q4 B) Find y' for the functions cos(xy) + 3*+cos ly+ In(xy) + log-7 dy

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Q: x²y" +xy' – y = T

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Q: cos² xy' = (1 + y²)

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Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

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Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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Q: Find H(−2) and H'(−2), where H(x) =

A: Here we have;  H(x)=∫-2xduu2+1

Q: g(x) = 2x−7+4 2x-π+4 o TT/2 sin² x g(t) dt

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Q: COST 1 f(x)= Jsinz 2 dt ise f'(0.257) aşağıdakilerden hangisidir?

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Q: Find dy/dx if y= cos-1 In(x+1)

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Q: Solve the integral equation X = Jo e*-fg(t) dt.

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Q: F(x) = J e2f sin² (3t)dt. Then F'(x) =

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Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

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

Q: Solve for y: a) ey+3 = x+ex b) ln(3y-4) = lnx+2

A: Use the lograthim and simplify.

Q: rez If F(x) = -7 sin t dt, then F'(x) =| %3D In x

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Q: If New Hampshire's population was 1.4 million in 2018 and there were 1.3 million motor vehicle…

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Q: u(x)=fo 2e eu(t)dt.

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Q: f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= -…

A: Given that Differentiate with respect to t           Therefore

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.