Solve the following problem: dh 10.3 + 0.002 ( 52.1h + 0) – 1.17(1 – sin 3t) = 0.0308, with h(0)=4 dt 10.3h, Where h denotes the liquid level (measured in meters) andt denotes the time (minutes). Find the liquid level at t=4 minutes using Euler's and Heun method. Assume step size of 1 minute. Plot your result. (Use calculator in radians)

Q: 1. Solve for y(t) for a given initial value problem as shown below: y" – 2y' + 5y = 8e'sin2t

A: according to our guidelines we can answer only first question and rest can be reposted

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Q: 3 the following first order ordinary differential equatio d. dy = (x²e³x + 6y)dx

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A: "Since you have posted multiple questions, we will answer the first question.  If you want the…

Q: Solve the initial – value problem: xtan sec2. dy C :y(3) =0 2. eesc?ydx-Vr sinydy =0 :y (In's)= 3.

A: we can solve these question by variable separation and homogeneous function technique of solving…

Q: 2. Use an appropriate method to find the general solution of the following differential equat (a) y"…

A: According to our guideline, we can solve only first question of multiple question. We solve here…

Q: ) Consider the following differential equation, with time domainte (0, 1): Sy - (' sin y(s) ds +t²,…

A: We are given the following differential equation with time domain t∈0, 1.…

Q: The following ordinary differential equation is given: dw /dx + 1.1w = wx^ 2 with w(0) = 1. Use…

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Q: Solve the following initial value problem: 1 dy + 2ry? + (2a²y – cos(y)). 0, y(1) = . dx

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Q: sinxsinydx + cosxcosydy = 0 %3D

A: To solve the given differential equation.

Q: Solve the following Exact Differential Equation with boundary value y(-1) = 2 (4y + 2t – 5)dt + (6y…

A: Given4y+2t-5dt+6y+4t-1dy=0y-1=2given differential  equation Mdt+Ndy=0 is exact if ∂M∂y=∂N∂t

Q: Solve by any method discussed in class. y(4) – 4y"=2t2 + sinh2t

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Q: 1. Solve the following differential equation dy dy + 2y dr = e" sin r dr2 by using the method of…

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Q: An RL circuit has an emf given (in volts) by 5sin 3t, a resistance of 6 ohms, an inductance of 0.4…

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Q: Solve for y(t) for a given initial value problem as shown below: y" – 2y' + 5y = 8e'sin2t

A:

Q: Approximate the solution of the equation x² – In(sinx) – 5 = o in the 3rd iteration of the Newton…

A:

Q: 2хydx + (y? — х?)dy %3D 0

A: Given- 2xydx+y2-x2dy=0 To Solve- The above differential equation using Exact Differential Equation.

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Q: (e). Solve the following initial value problem (1) 6y" – y' – y = 0, y(0) = 10, y' (0) = 0 (ii). dy…

A: Using linear differential equation for ex I) And variable separable method for ex ii)

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Q: Solve the following initial value problem. y(4) = - 2 sint+3cos t with y'''() = 8, y"(0) = - 3,…

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Q: Approximate the solution of the following initial value problem using Euler's method with step size,…

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Q: 13. Solve the initial value problem: d²s = -4 sin ( 2t –), s'(0) = 100,; s(0) = 0 %3D | dt² (Hint:…

A: sin(π/2 - x) = cos(x)

Q: 5. Solve the following second order differential equation dy + 9y = 4 – cos (3x) dx² by using the…

A:

Q: Find y (0.2) accurate up to five decimal places using Euler's Method by solving the initial value…

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Q: 1. Solve for y(t) for a given initial value problem as shown below: y" – 2y' + 5y = 8e sin2t

A:

Q: Solve the following initial value problem (t^2-12t+27)dy/dt=y with y(6)=1 On what interval is the…

A: Solution is given below:

Q: Give the general solution for each of the following Differential eequations y''-y'-6y=sin2t

A: Given that, The differential equation is following, y'' - y' - 6y = sin 2t We have to find the…

Q: 1. Solve the following differential equation dy dy - 2ug + 2y = e" sin x da? by using the method of…

A: Given:

Q: 5. Solve the following second order differential equation dy + 9y = 4 – cos (3x) dr2 by using the…

A: Answer

Q: 1. Solve for y(t) for a given initial value problem y"-2y' +5y = 8e'sin2t as shown below.

A:

Q: Solve for y(t) for a given initial value problem as shown belo y" -2y' +5y = 8e sin2t

A:

Q: Consider the following initial value problem: dy = 0.07 cos(t) with y(8.69) = 9.94 dt Using Euler's…

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Q: Solve the following initial value problem. y'" + 64y = sin 2x; y(0) = 1, y'(0) = 0

A: Given y''+64y=sin2x          ...........................1 y0=1, y'0=0 First consider the homogenous…

Q: Solve for y(t) for a given initial value problem as shown below. y" – 2y' + 5y = 8e*sin2t

A:

Q: Approximate the solution of the equation x2 – In(sinx) – 5= 0 in the 3rd iteration of the Newton…

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Q: Find the solution of the following initial value problem.

A: Given: h't=1+6sint; hπ3=-3 For finding solution of given initial value problem, we use variable…

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A: The differential equation

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.