Solve the IVP: y" + y = 6(t – 2m), y(0) = 0, y (0) = 1.

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A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: Solve the initial value problem dy — у %3D7 еxp(t) + 45 еxp(61) dt with y(0) = 5. y =

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Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: Find the general solution of

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: y" + y = sec x tan x

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Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

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Q: Integrate f(æ, y) = e2=² + 2y² over the domain {(x, y) | æ² + y? < 3}

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Q: Q. 4. Find the solution of dx -10y 4e using variation of parameter method. dx %3D

A: We have to solve given problem:

Q: dy + 2(t + 1)y² = 0, y(0) = – }. 4. Solve the IVP dt

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Q: Solve the initial value problem, dy y 1 y (1) =1 dx Use (i) Third order Runge Kutta method to find y…

A: NOTE  : Due to time limit answer of one method can be given, for others please ask in a different…

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Q: Q.3 Solve the Initial-value problem. dy %3D 3 y dt V1-t2

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Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

A: Given differential equation is  dydx=1+xy, y(0) = 1 To approximate the solution at x = 0.1 using…

Q: 2. Solve the IVP: dy + 2y = te-2t, y(1) = 0 dt

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Q: [-+] 5t dy 3.1는-51%3D-y dt

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

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

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Q: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* - х)dy %3D 0

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Q: 2(y-4x2) dx + x dy

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: Q₂) Compute Z² dz along the straight line from (0) to (4 + 4i), then verify your result by using…

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Q: solve the first order homogeneous  equation  dy/dx =y/x +(x/y) ^2 , given y(1) =2

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

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Q: Solve the initial value dy/dx = 1/x2 + 1 - 1, y(0) = 1

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Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

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Q: dx 2x - y dt dy

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Q: a) A vibrating spring can be modeled by the initial value problem: mx"(t) + bx'(t) + kx(t) = 0 With…

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Q: -2x 11/E valuate the integral 2 é V1-

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Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: Use Separation of Variables to solve the initial value problem. dy : (1 + y²) tan z, y(0) = v3 xp

A: solution of the given equation is tan-1y + log(cos(x)) = π3 detailed solution is given below

Q: dy Find the solution of = y (8 – ) satisfying the initial condition y(0) = 144.

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Q: Q3: Consider the initial value problem. dy d²y dy dt? + 0.25y = 0 dt (0) = b. dt y(0) = 2, %3D %3D…

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Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: A detailed solution is given below.   (As per our guidelines, we have to solve only 1st question)

Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Use the substitution t = -x to solve the given initial-value problem on the interval (-, 0). 4x?y" +…

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Q: Solve the DE by Homogeneous Equation 1. x y dx + (x² + y²) dy = 0

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