Solve the following ODEs using Euler's, Modified Euler's and 4th order Runge Kutta method. Use h=0.5 dq/dt + q = 4cos2t ; q(0)=1

Q: 3 Solve the following equations by Laplace transforms. dx (a) +3x =e-2t dt given that x =2 when t 0…

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Q: Solve the solution of the DE of the Gompertz function: dP = c In[P dt М In[P

A: We have a nonlinear ordinary differential equation :

Q: Consider the ODE dr 4t + 6/, x (0) = 1. dt Use Euler's method with h=0.5 to approximate the solution…

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Q: Find the formula for the function represented by the integral 1 -dt= 5t+1

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Q: 2. y" - 6y +9y = 2 sin 3x; y(0) = 1, y'(0) = 1

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Q: tody + y² = 0 dt

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Q: Use Laplace transforms to solve the following initial value problem. x''+x = 5cos6t, x(0)=1,…

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Q: Solve the following differential equation by using the Laplace transform techniques. d²x +8- dt² dx…

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Q: 3 Solve the following equations by Laplace transforms. dx (a) + 3x = e-2t dt given that x = 2 when t…

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Q: Solve the following ODE: x" + x = e-t with initial conditions x(0) = x'(0) = 0. Along the way, (1)…

A: Solution by using convolution theorem is given as follows :

Q: Use the Laplace transforms to solve the following initial value problem. x"+6x'+25x = 0; x(0)=2,…

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Q: Solve each of the following by Laplace Transform: dy -- 4 – 5y = e-34 sin(4t) ; y (0) = 3, y' (0) =…

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Q: use the Laplace transform to solve the given initial-value problem. Q. y′′−y =8sint −6cost, y(0)=2,…

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Q: Solve each of the following by Laplace Transform: dy 1.) +2- + y = sinh 3t – 5 cosh 3t ; y (0) = −2…

A: We have to find the solution to the given equation using the Laplace transformation.

Q: Solve the following equations by Laplace transforms. (b) 3x - 6x = sin 2t given that x =1 when t = 0

A: To find the Laplace transform of the given differential equation, first we take the Laplace…

Q: Reduce the following partial differential equation to a canonical form and hence solve it :…

A: The objective is to solve the partial differential equation, uxx-2sinxuxy-cos2xuyy-cosxuy=0

Q: Write the differential equation corresponding to the Legendre Polynomial P2(x) and verify that P2(x)…

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Q: 11 u(x) = atu(t)dt-

A: The given equation is, ux=116x+14∫01xt utdt                   .......1 On comparing the given…

Q: Solve the following equations by Laplace transforms. dx (a) +3x =e-2t given that x = 2 when t = 0 dt

A: Since every part is independent of each other so according to the guideline , I am going to solve…

Q: 10. Find the integral| dt. t* +81

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Q: Verify the initial value theorem of f(t) = 3 + 4 cos 2t. 7

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Solve the following differential equation using Laplace Transform

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Q: Solve the following differential equations by Laplace transform: y" + 2y' + 5y = 50t – 150, У (3)…

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Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

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Q: Solve for the Bernoulli DE 2t ds = s dt + 5t4s3 dt

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Q: Solve each of the following by Laplace Transform: 1.) +2. +y=sinh 3t — 5 cosh3t ; y (0) =−2 , ý (0)…

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Q: Use Laplace transforms to solve the following differential equations. a) + 5y = 3 , given that y = 1…

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Q: The following is an first-order ODE dy = (3y = 4x – 2)0.5 dx Where y(1) = 1 Please calculate y at x…

A: Given ODE: dydx=(3y+4x-2)0.5 with y(1)=1 To calculate y(2) using a step size h=0.5 via (a) Euler's…

Q: y" - 10y'+ 9y = 5t, y(0) = -1, y' (0) = 2

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Q: Solve the following initial-value problems (IVP) using the Laplace transform method. Show complete…

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Q: Solve the following equations by Laplace transforms. dx - dt + 3x = e-2t given that x = 2 when t 0

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Q: Solve the following non-homogeneous linear ODE of first order dy 2y + dx sin x

A: Given, dydx+2xy=sinxx To solve the above differential equation.

Q: Solve the following ODE using Laplace Transforms Method: y'+y=2sinx when y(0) = -1

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Q: Use Laplace transform to solve the initial value problem x" - 9x = e;x(0) = 1, x'(0) = –1

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Q: - Solve the linear ODE using an Integrating Factor. x². dy dx + 2xy = 3sin(8x)

A: solution is given below

Q: Solve the following ODE in the range [0, 0.2] using h dy y(0) = 2, -t+y=0, dt² = 0.1 with explicit…

A: Given that d2ydt2-t+y=0 with condition y0=2, dydt0=0 Solve using Euler's method when step size is…

Q: Compute the value of the following integral: 00 (t−7) cos (¹) 8 (t-1)dt 00 where 8(t) is the unit…

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Q: Solve the following differential equation by using Laplace and inverse Laplace transform: у" — у'+…

A: Taking laplace transform on both sides

Q: Solve the following initial value problem by using Laplace transforms: 1"(t) + 9x = cos 3t, r(0) =…

A: Solution of ordinary differential equation with constant coefficients using Laplace transform:…

Q: Solve the following differential equations by Laplace transform: y" – 3y' + 2y = 4e2t, y(0) = -3,…

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Q: select a method for solving the particular solution of following ODE d?y 4x + 12y 0 | O Power series…

A: This differential equation can be solve using Power series method Power series solution is

Q: %3D are expressio at %3D = 0, ...

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Q: Use Laplace transforms to solve the initial value problem x"+ 4x = 0; x(0)= 5, x'(0)=0

A: Consider the provided initial value problem, x''+4x=0,x0=5, x'0=0 To solve the provided initial…

Q: Solve the following DE, using Separable method. y'In ly| +x*y =0.

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Q: Solve the following DE using Separable method. 2y' = x(1- y')

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Q: 2. w(p) – 3 w(v)dv = 10 cos 7p

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Q: Use Laplace transforms to solve the following initial value problem. x" + 6x' + 25x = 0; x(0) = 5,…

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Q: ) Solve the following Second order Ordinary Differential Equation (ODE) using Laplace Transform:

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Q: Solve each of the following by Laplace Transform: 1.) ď² y +2 + Y dy dt - = sinh 3t - 5 cosh 3t dt²…

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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.