F(2) = (2t – 1)° dt using the Fundamental Theorem of Calculus.

Q: y"- y'- 2y = 0; y(0) = -2,

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Q: у" - у'— бу %3D 2, у (0) %3D 0, y'(0) = 0

A: Given that     y" - y' -6y = 2 , y(0)=0 , y'(0) = 0

Q: Solve using Laplace Transform: y +y = sin 2x ; y(0) = 2, y'(0) = 1

A: Given differential equation isy''+y=sin2xWhere initial conditions arey(0)=2,y'(0)=1The given…

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: Solve using Laplace Transforms y"+4y = t-2 sin t; y(0)=-1, y'(0)= 2,

A: given differential equation isy"+4y=t-2sinty(0)=-1y'(0)=2applying laplace transformLy"+4y=Lt-2 sin…

Q: (a) Solve for the initial value problem by using Laplace transforms method у"- у'- бу %3DSin 2t y(0)…

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Q: Solve by Laplace transform method. y '"-3 y '+2 y = 4 , where y(0) = 2; y'(0) = 3.

A: The given differential equation is  y''-3y'+2y=4,   y(0)=2 , y'(0)=3 Laplace transform of few…

Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: Use the differential operators y'"-5y'+6y=e* %3D

A: Given that a second order non homogeneous differential equation and find its solution. Here i…

Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

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Q: Solve by Laplace transform method x' = 2x – 2y у'3 х — у — cos t x(0) =,y(0) = 3 4

A: Solution: The system is x'=2x-2y y'=x-y-cost x0=35,  y0=45

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find the total differential. w = e3y cos(5x) + z5 ||

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Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2  +  ∂2z ∂y2  =…

A: Given Laplace’s equation is

Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

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Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: b) f(x) = In(1 – 3x) %3D c) f(x) = cos(t³) dt

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Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If y=2x2−1, and dx/dt=5 when x=14, what is…

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Q: y = tan (5t - 21 +1)

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Q: . Determine the Laplace transform of the differential equation 3y" – y' = et5 - 9y" + 4y

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Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: Determine the Laplace transform of the differential equation 3y’’’ – y’ = e-3t t5 - 9y’’ + 4y With…

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Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: Prove f(x,y)=ln(x2+y2)1÷2  by laplace equation

A: Given: The function, fx,y=lnx2+y2 and the Laplace equation, ∂2f∂x2+∂2f∂y2=0.

Q: 1. xy + z2

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Q: Solve and prove that the solution derived from Laplace Transform of Derivatives and the initial…

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Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Given Differential equation : y'=x-xy  ,(1,0) dydx=x(1-y) Now we solve the equation by separation of…

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Laplace under initial conditions x '+ y' + x= 0 and x '+ 2y' = 1 equation system x(0) = y (0) = 0…

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Q: 10. Show that the function f(x, y,z) = 2z³ – 3z(x² + y²) satisfies the Laplace Equation,

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Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

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Q: Sketch the slope field for dy/dt=y2-4. How do the solutions behave as t approaches infinity? Is end…

A: Given differential equation dy/dt=y2-4. Sketch of the given differential equation is shown below :

Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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Q: 2. u(x)= secx+à So u(1)dt.

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: Solve using Laplace transform y" – 6y' +13y=0, y(0)=0, y'(0)=-3

A: Using Laplace transform of derivatives

Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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Q: Use the Laplace transform to solve the initial value problem. y''+ 36y = sin(6t), y(0) = 1, y'(0) =…

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Q: Solve using Laplace transform method: y + y = 1 y(0) = 2 [y' (0) = 0

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Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: Can i get help step by step please

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Q: Solve using Laplace Transforms. y'" + 2y' + 3y = u2n(t) y(0) = y'(0) = 0

A: We will find out the required solution.

Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

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