1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

Q: A point is moving along the graph of a given function such that dx/dt is 3 centimeters per second.…

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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: Show that y(t) =t-2 ln t is a solution to ty"+5ty' +4y 0. (where t> 0)

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Q: Use Euler's method with h = 0.25 to compute approximate value of y(1) for the IVP: (a) dy 1 = y sin…

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Q: Solve the Bernoulli equation for y. dy = 2y + y°. dt Use the following initial condition: y(0) = 1.…

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Q: A point is moving along the graph of a given function such that dx/dt is 3 centimeters per second.…

A: Given: dxdt=3 cm/sec The function of y is: y=3x2+2 Differentiate both sides with respect to t:…

Q: (k) / te'dt (1) / e' sin(t) dt (i) e2t dt dt 1+ t2

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Q: Let the following equation d ^ 2y / dt ^ 2 + 0.5cos (y) dy / dt + sin (y) = 0 with y (0) = π / 2…

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Q: Can you help me step by step with this problem?

A: Apply exponent rule for the exponent then use chain rule Exponent rule: d/dx(x^n)=n*x^(n-1)Chain…

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 dy/dt. y = (t-3/4 sin t)4/3

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Q: 16. t 31²y = cos t, y(T) = 0 dt

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Q: Find for y = | 12t°dt. dx

A: Given: y=∫0x12t3dt

Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

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Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the given value of the parameter. dx…

A: Follow next step

Q: The general solution dx/dt t+x of t > where t > 0, is x(t) =

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Q: b. g(x) = [ cos(r*)dt x²+5x F(x)= [,(6r* +6e° )dt с. 6t +6e" dt

A: We have to find derivative

Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

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Q: 69. Find the value of dr/dt at t= 0 if r= (02 + 7)3 and 0?t + 0 = 1.

A: Given: r=(θ2+7)13θ2t+θ=1drdt|t=0=?

Q: (2) y(x) = 1+1 So (1 – 3xt)y(t) dt

A: Given that the equation is yx=1+λ∫011-3xtytdt Let take Kx,t=1-3xt Then yx=1+λ∫01ytdt-3xλ∫01tytdt. So…

Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy dx + x + 4y = 10; æ dt - y = 0 dt

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Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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Q: Solve the Bernoulli equation for y by making the substitution u = dy = 4y + y°. dt Use the following…

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Q: 3. The length of the curve determined by the equations x =t and y=t from t=0 to t= 4 is a. b. 2[VF…

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Q: dy 3 4-1+2у, dt (0) = 1

A: Given dydt=4-t+2y   ; y(0)=1  with h=0.1

Q: a. S ya +1 b+y+cya+1 b. ft² cos 3t dt dy where a 0 and c = 1/(a + 1).

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Q: The acceleration of a particle moving back and forth on a line is a = d2s/dt2 = pai ^2 cos pai t…

A: Given information:

Q: B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time…

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Q: Solve the following initial value problem for r as a function of t. dr = 2e 'i - 5e -'j+ 12e 2tK dt?…

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Q: 3 + 1)'0 dy calculate dx Given y = dt

A: From the fundamental theorem of calculus, ddx∫0xf(t)dt=f(x) And from the chain rule,…

Q: dT equation dt k(T A).

A: we have been given the differential equation dTdt=k(T-A) this is the first-order linear differential…

Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the parameter t 6. dt TO -/-

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Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt dy

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Q: t2 + 9 V8 - t dy if y = In dt Find dy dt

A: Given equation is y=lnt2+98-t. Compute the derivative with respect to t.…

Q: A point is moving along the graph of a given function such that dx/dt is 3 centimeters per second.…

A: Given: A point is moving along the graph of a given function such that  dxdt  is 3 centimeters per…

Q: find dy/dt. y = (t tan t)10

A: We will use the power rule, chain rule and product rule.

Q: Solve the Bernoulli equation for y. dy 2y + y*. dt Use the following initial condition: y(0) = 1.

A: We need to solve the Bernoulli equation for y. To solve given differential equation first using…

Q: Q5) Solve the equation dx dt² 1 y (x,0)=sin лx ,t=0,0≤x≤1 8 and dy (x,0) =X at 11 with y (0,1)=y…

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Q: Find the general solution of the given equations below: 1) dy dy 3+ 2y = e' sin(t) dt

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: 1. Find the function y(t) satisfying y' = ey-t(1 +t²) sec y with y(0) = 0.

A: Given: The differential equation y'=ey-t (1+t2) sec y, y(0)=0.

Q: Q4:B. Solve the following differential equation using Laplace transforms. dy dy +2 +2y e dt y(0) =…

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Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: use Euler’s Method to approximate the given value of y(t) with the time step h indicated. y(2);…

A: Here we solve the given function by using the Eular’s method:

Q: psin(z) (c) y = [ dt t+1

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Q: An object moves in one dimension with avelocity in m/s given by v(t) = 8 sin ∏t + 2t. Find its…

A: Given: The velocity of an object in m/s is given by  v(t)=8sinπt+2t Time interval is t=0 to t=10

Q: Please show all work

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Q: Solve the Bernoulli equation for y by making the substitution u = y?. dy 5y + y'. dt Use the…

A: A differential equation is an equation that relates one or more functions and their derivatives…

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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