- A tank contains 800 gal of water in which 200 lb of salt is dissolved. Two gallons of fresh water runs in per minute and 2 gal of the mixture in the tank, kept uniform by stirring, runs out per minute.
- Form a differential equation for the amount of salt in the tank as a function of time.
- How much salt is left in the tank after 5 hours?
- A thermometer, reading 10^\circ\mathrm{C}, is brought into a room whose temperature is 23^\circ\mathrm{C}. Two minutes later the thermometer reading is 18^\circ\mathrm{C}.
- Use Newton's Law of Cooling to model the change of the thermometer reading with time.
- How long will it take until the reading is practically 23^\circ\mathrm{C}, say, 22.8^\circ\mathrm{C}?
- Solve the following initial value problem (IVP) and make a reasonably accurate sketch of the solution:
2y^\prime + y^3 = 0;\quad y(0)=1
- Solve the following ODEs:
- \left[\sin(y)\cos(y)+x\cos^2(y)\right]\,dx + x\,dy=0
- e^y\,\left[\sinh(x)\,dx + \cosh(x)\,dy\right]=0
- (x^2+y^2)\,dx - 2xy\,dy =0
- \left(\cos(xy)+\dfrac{x}{y}\right)\,dx + \left(1 + \dfrac{x}{y}\cos(xy)\right)\,dy=0
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- Under what conditions for the constants A,B,C,D, is the following ODE exact?
(Ax+By)\,dx + (Cx+Dy)\,dy=0 - Solve this exact ODE.
- Under what conditions for the constants A,B,C,D, is the following ODE exact?
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- Solve the ordinary differential equation: y^\prime\tan(x)=2y-8.
- Sketch the family of solutions given by the general solution to the above ODE.
- Give the particular solution to the above ODE such that y=0 when x=\pi/2.
Saturday, 3 September 2011
ODE - Assignment 1
Due Date: September 9 September 12
Labels:
assignment,
B.Tech.,
ODE
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