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(1) A tank initially contains 300 liters of brine containing 30 kg of salt. Brine with 10 kg of salt per liter flows into the tank at a rate of 15 liter per second and the well-mixed solution flows out at a rate of 10 liter per second. Let Q(t) be the amount of salt in the tank at time t. Using the given information, pick the ODE that governs the time evolution of Q(t). dQ 150+ 10- Q(t) 300+ 5t dt dQ dt dQ dt dQ dt Q(t) 300 + 5t 150-10- = 150- Q(t) 300 + 5t Q(t) 300 =150-10-

(1) A tank initially contains 300 liters of brine containing 30 kg of salt. Brine with 10 kg of salt per liter flows into the tank at a rate of 15 liter per second and the well-mixed solution flows out at a rate of 10 liter per second. Let Q(t) be the amount of salt in the tank at time t. Using the given information, pick the ODE that governs the time evolution of Q(t). dQ 150+ 10- Q(t) 300+ 5t dt dQ dt dQ dt dQ dt Q(t) 300 + 5t 150-10- = 150- Q(t) 300 + 5t Q(t) 300 =150-10-

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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5. Answer all the questions. Justification required. (1) A tank initially contains 300 liters of brine containing 30 kg of salt. Brine with 10 kg of salt per liter flows into the tank at a rate of 15 liter per second and the well-mixed solution flows out at a rate of 10 liter per second. Let Q(t) be the amount of salt in the tank at time t. Using the given information, pick the ODE that governs the time evolution of Q(t). dQ Q(t) 150+10- dt 300+ 5t dQ dt dQ dt dQ dt = 150-10; = 150- Q(1) 300+ 5t Q(t) 300+ 5t Q(t) 300 150-10- (2) Suppose we have a second-order constant-coefficient inhomogeneous ODE with a particular solution Up = = cos(r). If we know that the associated homogeneous ODE has two linearly independent solutions y₁=e* and 2 = re, then what is the general solution to the inhomo- geneous ODE? Oy(x) = e² + xe + cos(x) O y(x) = ce + c₂ze" + c3 cos(x) where C₁, C2, C3 are are real numbers. Oy(x) = ce + c₂re + cos(x) where c₁, c₂ are real numbers. O y(x) = ccos(z) where e is a real number.
Transcribed Image Text:5. Answer all the questions. Justification required. (1) A tank initially contains 300 liters of brine containing 30 kg of salt. Brine with 10 kg of salt per liter flows into the tank at a rate of 15 liter per second and the well-mixed solution flows out at a rate of 10 liter per second. Let Q(t) be the amount of salt in the tank at time t. Using the given information, pick the ODE that governs the time evolution of Q(t). dQ Q(t) 150+10- dt 300+ 5t dQ dt dQ dt dQ dt = 150-10; = 150- Q(1) 300+ 5t Q(t) 300+ 5t Q(t) 300 150-10- (2) Suppose we have a second-order constant-coefficient inhomogeneous ODE with a particular solution Up = = cos(r). If we know that the associated homogeneous ODE has two linearly independent solutions y₁=e* and 2 = re, then what is the general solution to the inhomo- geneous ODE? Oy(x) = e² + xe + cos(x) O y(x) = ce + c₂ze" + c3 cos(x) where C₁, C2, C3 are are real numbers. Oy(x) = ce + c₂re + cos(x) where c₁, c₂ are real numbers. O y(x) = ccos(z) where e is a real number.
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