Math Solutions

(Solution Library) (a) Consider the first order ODE (dy)/(dx)=e^-4x-3y, y(0)=1. Solve the above ODE above, using the integrating factor method to obtain an exact

Question: (a) Consider the first order ODE

\[\frac{dy}{dx}={{e}^{-4x}}-3y,\,\,\,y(0)=1.\]
  1. Solve the above ODE above, using the integrating factor method to obtain an exact solution. Evaluate the exact solution at the point \[x=0.5\] .
  2. Use Euler’s method to obtain an approximate solution of the above ODE at \[x=0.5\] , using \[{{x}_{0}}=0\] and step size \[h=0.1\] . Work to 3 decimal places.

(b) A uniform circular hoop of mass 10 kg and radius 0.5 metres starts from rest and rolls, without slipping or falling over, and with its plane vertical, down a line of greatest slope of a fixed plane which is inclined at an angle \[{{45}^{o}}\] to the horizontal.

  1. Calculate the linear acceleration of the centre of the hoop.
  2. Find the linear velocity of the centre of the hoop once the hoop has rolled a distance of 1 metre.

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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