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For Problems 21-24, verify that the given
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Differential Equations and Linear Algebra (4th Edition)
- (b) If y=ae", express t in terms of a and y.arrow_forward4. The equation of motion of a particle is s = t* – 2t3 + t2 – t, where s is in meters and t is in seconds. a) Find the velocity and acceleration as functions of t. b) Find the position, velocity, and acceleration after 1 second.arrow_forwardA mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv ' dt exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.arrow_forward
- find the homogenous linear equation satisfied by the following functions y = x2 sinx+ e5xarrow_forwardfind the derivative of (23 + j) O 23 + j O 223 +j O 625 + j6z? O 325 + j3z2arrow_forwardA hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second. y = Hint: e^(-16t)(((1/(2sqrt(2))*e^(8sqrt(2)t)-(1/(2sqrt(2))*e^(-8sqrt(2)t))arrow_forward
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