Pracex1

Pracex1 - A 20 B 80 C 40 20 e D 400-360 e-1 E 400 360 e 2 8...

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MA 262 Midterm 1 Practice Problems 1. Find all values of r so that x r a solution of the equation x 2 y 00 - 2 xy 0 + y = 0 2. An implicit solution of y 0 = 2 x y + x 2 y is A. y 2 = 2 ln(1 + x 2 ) + C B. y 2 = C ln(1 + x 2 ) C. 1 2 y 2 = ln x 2 + C D. y 2 = ln(1 + x 2 ) + C E. 1 2 y 2 = ln | 1 + x | + C 3. Find the implicit solution of the equation y 0 = x 2 + 3 y 2 2 xy 4. The value of a so that the solution to the initial value problem y 0 - 2 y = e - 2 t , y (0) = a is bounded (i.e. not tending to inﬁnity as t → ∞ ) is A. a = 0 B. a = 1 C. a = - 1 D. a = - 1 4 E. None of the above 5. Find the orthogonal curves to the family y = Cx 4 . 6. Solve the diﬀerential equation (2 xy + x 3 ) dx + ( x 2 + y 3 + 2) dy = 0 , y (0) = 2 1

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7. A tank initially contains 40 ounces of salt mixed in 100 gallons of water. A solution containing 4 oz of salt per gallon is then pumped into the tank at a rate of 5 gal/min. The stirred mixture ows out of the tank at the same rate. How much salt is in the tank after 20 minutes ?
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Unformatted text preview: A. 20 B. 80 C. 40 + 20 e D. 400-360 e-1 E. 400 + 360 e 2 8. Find the general solution of the equation y 00 = y y, y (0) = 0 , y (1) = 1 9. Find all values of a and b so that the system x 1 + x 2 + 2 x 3 = a 2 x 1 + 2 x 2 + 3 x 3 = b x 1 + x 2 + x 3 = 3 is consistent, and solve it in that case. 10. Compute the reduced row row-echelon matrix that is row equivalent to A = ± 2 1 1 0 1-1 ² 11. Compute A-1 where A = 0 1-1 1 1 1 1 2-1 12. Find all constants a and b so that the matrix A = a 1 1 1 b 1 b 1 2 has rank 2. 2...
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Pracex1 - A 20 B 80 C 40 20 e D 400-360 e-1 E 400 360 e 2 8...

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