Consider the following initial value problem y' (t) = y² + y t where y' = and initial conditions y(1) = −2 dy dt' Estimate y(1.2) with step size h = 0.2 using the following four methods (hand calculation) a) Forward Eular Method b) Heun's Method c) Mid-point Method d) Fourth-order Runge-Kutta Method

Q: ちad; mpliいyiy txy = x -x +2

A:

Q: Given that fCx) = x"hc) h'(1)=6 Calculate f'(-1) =

A:

Q: Suppose dy/dt= 6 ze^(3z^2+2) and y(0)=4. what is y(1)?

A:

Q: consider y'=-2y,y(0)=1 and analytic solution is y(x)=e^-2x a.Approximate y(0.1) using two steps of…

A:

Q: and the condition y(0) = 1. y(t) = e^(t^2)(1+2t^3) dy dt -2ty=-61²e¹²

A:

Q: · Sº t³ dt then f'(x)= If f(x) = and f'(-2) =

A:

Q: Find the general solution to the following Bernoulli Equation: dy/dt - y/2t^(2) = te^(-1/t) / y…

A:

Q: y'' + p(x)y' + q(x)y = 0Here why only two initial conditions?

A:

Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

A:

Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

A:

Q: y(2)=3/0 y (2) = 3/1 below. Use the graph to estimate the values of yo and 1. 5 "

A: Follow the steps.

Q: dy/dx=3x^2+1 with y(1)=2. Estimate y(2) by Euler's method

A: given differential equation dydx=3x2+1 with initial condition y1=2 claim- estimate y2 by euler's…

Q: 4: A:Find the solution of the initial value problem (d^2 y)/(dx^2 )+5 dy/dx+6y=0□( ) y(0)=2, And…

A: Given A. d2ydx2+5dydx+6y=0  ;  y0=2 and dydx=0 B. 2yz-3lnz=2x+5y

Q: 19 If f(x) = t dt then %3D f'(x) =

A: Given that  f(x) = ∫x19t4 dt  Here we have to find f'(x) .

Q: Which of the followig functions  are solutions for the differantial equation y"-7y'+6y=0  I…

A:

Q: 2) A population is changing over time at a rate modeled by the function P'(t) = 4te08(1-²) where t…

A:

Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

Q: 1.) xy3dx + (y+1)e^-xdy = 0 2.) dx/dy = x-2ycotx

A:

Q: Find the extrema y = y(x) of J(y) = [' (y)² √/1 + (y^)²dx, _y(0)=1=y(1). e is a minimum or maximum?…

A:

Q: Verify whether or not y(t) = ce^(2t)−1/4 e^(t) is the general solution to the DE dy/dt = 2y + 1/4…

A:

Q: Find the general solution to the following Bernoulli Equation: dy/dt - 3 * sqrt(t) * y = sqrt( t *…

A:

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

A:

Q: (1)=2x+5 y(2)=x^2-8x+17   1. find the value of y(2) at its minimum, and the rate of change of…

A:

Q: Fnd the solution to the initial value problem: dy/dt = (2t)/(y+t^(y)), y(0) = -2

A: Here the question should be , dy/dt=(2t)/(y+(t^2)y ) , y(0)=-2. I have solved it accordingly .…

Q: Find h'(x) if rsin 2x t2 cost dt h(x) = J3 %3D

A:

Q: Given the equation y = 5 In| 6y | Find the Implicit derivative " dy/dx" of the function. You will…

A: We can find the derivative as below.

Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

A: