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- Solve the following 3rd order equation: y'"+2y"-y'-2y=0arrow_forward20 40x-x² x²+y² dydx =arrow_forward4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tut 80x + 1000x = 2500 cos where r = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of time t (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (a) Find the general solution to this nonhomogeneous ODE. Note that your answer will have a term in it which is a function of v.arrow_forward
- Two tanks are connected as in Figure 1.6. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to tank I at the rate of 5 gallons per minute, Tank 1 has an output that discharges brine into tank 2 at the rate of 5 gallons per minute, and tank 2 also has an output of 5 gallons per minute. Deter- mine the amount of salt in each tank at any time. Also, determine when the concentration of salt in tank 2 is a minimum and how much salt is in the tank at that time. Hint: Solve for the amount of salt in tank 1 at time t and use this solution to help determine the amount in tank 2. S prl min: 12 Ih gel S gil tain Tauk pal minarrow_forwardSolve the following Clairaut equation y=xy'+(y')^2arrow_forwardHelp with parts a through e, having some difficulty with the phase lines.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,