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Unformatted text preview: x 2 dx dt = 2 t +1. Give your answer with x as an explicit function of t , if possible. 4. (18 points) Solve the diﬀerential equation dy dx + 2 x x 2 + 1 y = 4 x . Give your answer with y as an explicit function of x , if possible. TWO MORE PROBLEMS ON BACK 2 5. A 500 gallon tank initially contains 100 gallons of water into which 5 pounds of salt has been dissolved. Pure water ﬂows into the tank at 5 gallons per minute and the well-mixed salt water ﬂows out of the tank at 1 gallon per minute. Let x ( t ) represents the pounds of salt in the tank at time t . (a) (3 points) After how many minutes will the tank overﬂow? (b) (10 points) Give an equation for dx dt but do not solve the equation. (c) (3 points) State the initial condition, x (0). 6. (20 points) Solve the initial value problem 2 y 00 + 3 y-5 y = 0; y (0) = 10; y (0) = 3...
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- Spring '09
- Trigraph, Boundary value problem, Gallon