Let y(t) be the solution to y=7te−y satisfying y(0)=2. (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4),…,y(1.0). (b) Use separation of variables to find y(t) exactly.(c) Compute the error in the approximations to y(0.2),y(0.6), and y(1).

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Let y(t) be the solution to y=7te−y satisfying y(0)=2. (a) Use Euler&#039;s Method with time step h=0.2 to approximate y(0.2),y(0.4),…,y(1.0).  (b) Use separation of variables to find y(t) exactly.(c) Compute the error in the approximations to y(0.2),y(0.6), and y(1).

autormtak0w · Accepted Answer

Step 1  Let y=f(t,y),y(t0)=y0 be given IvP  The by Eulers

Ethan Sanders · Accepted Answer

Step 3  y=dydt7te−y - (1) y(0)=2 -(2)  ⇒dye−y=7tdt  ⇒∫eydy=∫7tdt+c  ⇒ey=7t22+c  Using (2) we get,  e2=c  ∴ey=7t22+e2  ⇒y(t)=loge[7t22+e2]

karton · Accepted Answer

Step 4 ∴y(0.2)=2.0188∴|(y(0.7)−y1)=|(2.0188−2)=0.0188now y(0.6)=2.1574∴|(y(0.6)−y3)=|(2.1574−2.11078)=0.04662∴y(1)=2.3878∴|(y(1)−y5)=|(2.3878−2.3351)=0.0527

Let y(t) be the solution to y = 7te^{-y} satisfying

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