the Chain Rule to find dz/dt. z = cos(x + 7y), x = 5t5, y = 3/t dz %3D dt -sin 5 + 21 254 21 II

Q: (a) Find the Laplace transform Y(s) of the differential equation -ty" – y – 4ty = 0, y(0) = 5, y/(0)…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Use Fourier Transform to solve the differential equation y' – 3y = H(t)e-3t Hint: The Fourier…

A: Given the given differential equation is y'-3y=Hte-3t. Apply Fourier transform formula.…

Q: differential eqation, find general solution for dy/dt = −3y + 4 cos 2t   thank you.

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Q: Current Attempt in Progress dz Use an appropriate form of the chain rule to find dt 1 y = 7t z = 9…

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Q: dx for 4xy - 5x + 2y3 = - 42, with the conditions dt = - 6, x=2, y= - 2. dt Assume x and y are…

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Q: Q) Use the chain rule to express dy / dx in terms of x and y for the :following y =1-! 1 t = 1-x and…

A: Consider: y=1-1t and t=11-x. Calculate dydxin terms of x,y at x=2. Calculate dydt and dtdx using…

Q: The differential equation dx/dt = 100x(x- 5)+ s models a population with stocking at rate s.…

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Q: dx/dt=x(1-x)  (Solve the DE using solution for linear and Bernoulli’s equations only.)

A: Solve the DE using solution from linear and Bernouei's eqn only…

Q: dz Use the chain rule to find Ət z = tan (x – 8y), x = s cost, y = e² •Int Se dz 1+(x²– $y}² dt dz -…

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Q: 7. Which of the folowing differential equationsis ex act? a. y°e*dx + e*dy = 0 c. sin x sin ydx +…

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. Given: (a). y2exdx+exdy=0 So,…

Q: Q3. Calculate L{e-# cos(2t – 1)} dy 1+ x Q4. Find Integrating Factor for the linear DE y = cos(x)…

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Q: Question3: Solve the differential equation using the Laplace transform y" + 3y' – 4y = cos(2t); y(0)…

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Q: Linearize the following differential equation about point, x= T/3. d²x +2 dt? dx + sin x=0 dt

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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: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: y" + y = e sent,

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Q: dy dx with cly --2 and y=1 X =0 dx2 dx

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Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: The Integrating Fachor for the DE y dx- Ge-2x)Jdy -2y None of These

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Q: dy The integrating factor of Linear differential equations + y x 2 tan a = secr is dæ O In sin 2r O…

A: The given differential equation is: dydx+y×2tanx=sec2x …1

Q: Use the differential dy to approximate Ay when x changes as indicated. y = V 3x – 2; from x = 2 to x…

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Q: y" – y' – 2y = 4t², y(0) =1 y'(0) = 4 I| |

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Q: (a) Find the differential dy. y = cos(Tx) dy = (b) Evaluate dy for the given values of x and dx.…

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Q: y" + 4y" + 9y' + 10y = e-dsind y"(0) = y'(0) = y(0) = 0 %3D

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Q: Consider dx/dt = t − x, x(0) =1. a) Use Euler’s method with step sizes h ? 1, 1/2, 1/4, 1/8 to…

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Q: (a) Find the Laplace transform Y(s) of the differential equation -ty" – y – 4ty = 0, y(0) = 5, y/(0)…

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Q: nd a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy -3x + 5y° = - 210, with the conditions dt…

A: Given: 4xy-3x+5y3=-210 with the condition dxdt=-15, x=5, y=-3 To find: differentiate the given…

Q: Consider the autonomous differential equation dy/dx = fy), where the graph of fis given. Use the…

A: Given  The autonomous differential equation is... dy/dx=f(y) Let us draw the given graph f

Q: Find the differential equation such that y(x) = (x + 10)°(c,cos(2ln(x+ 10)) +c,sin(2ln(x+ 10))) d²y…

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Q: df Q4) A) Find dx by using chain rule if f = , u=-1 , x=-1 u+1 B) Evaluate the following integral:…

A: A) To find the derivative of the given function f=u-1u+12 with u=1x2-1

Q: dM 15) М? — 5М + 6 М (1) — 4 dx

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy - 7x+4y3 = - 92, with the conditions dt =…

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Q: Transform into first order linear form the differential equation (1 cos z) y' sinz (sin z + sin…

A: The given differential equation is                                  (1+cos x)y'=sin x (sin x+sin x…

Q: Transform into first order linear form the differential equation (1 cos z) y' sinx (sin r + sin…

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Q: The differential equation formed by eliminating the arbitrary constant A: y = A cos z +1 is O y tanz…

A: Given equation is, y=Acosx+1

Q: dy +4 dt -4w y(t - w) e dw = 8, y(0) = 0. a. Use convolution and Laplace transforms to find the…

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Q: y2 Use the modified Euler Method to solve the ODE = dx subject to y = 1 when x = 0 1+x on the…

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Q: dx = -18, x 6, y= -3. for 3xy 7x+6y3 = -258, with the conditions Assume x and y are functions of t.…

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Q: (a) Find the Laplace transform Y(s) of the differential equation ty" + y + 4ty = 0, y(0) = 3, y (0)…

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Q: Solve the differential equation using Laplace Transform and Inverse Laplace transform y" – 4y' + 4y…

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Q: ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0…

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Q: dy dx Assume x and y are functions of t. Evaluate for 3xy-3x+2y³ = -78, with the conditions = -6,…

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Q: Qu 1 a). Determine the LaPlace transform of the differential equation y"- y = e2 ; y(0) =0 and y"(0)…

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Q: Which differential equation is variable separable? (A) xy dx + (x² + 1) dy=0 (в) (х2+ у) dx - Зху…

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Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

A: Here we use table of Laplace transforms and some properties of Laplace transform.