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differential equiations
6. Consider the set of curves 4x2 +9y2 = C where C is an...
The orthogonal trajectories of the family of curves 2 = 2y - 1+ Ce"where is an...
The orthogonal trajectories of the family of curves 2 = 2y - 1+ Ce"where is an arbitrary constant is given by the family of curves 2y=**** where x arbitrary constant º + where x ban arbitrary constant None of them + y = + where Karbary.com + is where is an arbitrary constant
The orthogonal trajectories of the family of curves 22 = 2y - 1+ Ce-24, where is...
The orthogonal trajectories of the family of curves 22 = 2y - 1+ Ce-24, where is an arbitrary constant, is given by the family of curves None of them * + y2 + k where k is an arbitrary constant 4 24 xy? + k where k is an arbitrary constant 4 x+y= + k where k is an arbitrary constant 4 O 2? + y 24 4 + k where K is an arbitrary constant
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0)...
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0) = x3 + 1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
Consider the partial differential equation, with the initial condition: 1 2 cup +3cºu, = 9x²y?, u(x,0)...
Consider the partial differential equation, with the initial condition: 1 2 cup +3cºu, = 9x²y?, u(x,0) = x3 +1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
Question 3 The orthogonal trajectories of the family of curves go? = 2y - 1+ Ce-2y,...
Question 3 The orthogonal trajectories of the family of curves go? = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves + kwhere is an arbitrary constant o 2 + y2 + k where K is an arbitrary constant 4 None of them C zy +k where x is an arbitrary constant 4 24 2 + y = + k, where k is an arbitrary constant 4
please show work 3 pts Question 3 The orthogonal trajectories of the family of curves ?...
please show work
3 pts Question 3 The orthogonal trajectories of the family of curves ? = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves way + where k is an arbitrary constant 4 x + + where K is an arbitrary constant 4 None of them 2y + where K is an arbitrary constant 4 o 22 + y = + k, where k is an arbitrary constant 4.
Question 3 3 pts The orthogonal trajectories of the family of curves x2 = 2y -...
Question 3 3 pts The orthogonal trajectories of the family of curves x2 = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves None of them 2 + y2 Alt + k where k is an arbitrary constant 4 xy? + k, where k is an arbitrary constant 4 O x? y + k where k is an arbitrary constant 4 x2 + y = + k, where K is an arbitrary constant...
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a d...
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a direction (expressed as a unit vector) for which the directional derivative at the point (1,2) is 0.
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate...
1- 2- 1. Consider the family of curves y = 22 + c family of orthogonal...
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1. Consider the family of curves y = 22 + c family of orthogonal trajectories. Sketch some curves from both families on the same graph. 3. A tank starts with 10 L tank at a rate of 1 L/min. Th ow long it takes for Thin. The well-stirred m with 10 L of water into which 20 g of salt is poured. Pure water flows into the ta rate of 1 L/min. The well-stirred mixture flows out at...
1. Given: the ellipse with equation 4x2 9y2 36 Use methods of calculus to find each of the follow...
1. Given: the ellipse with equation 4x2 9y2 36 Use methods of calculus to find each of the following, that is, set up an expression involving a definite integral. Evaluate using a calculator unless otherwise stated. a) Find the area of the ellipse, to three decimal places (10) b) Express the equation of the ellipse in polar form and find its area, to three decimal places. (10) c) The area of an ellipse can be found by using the formula...
The orthogonal trajectories of the family of curves 2 = 2y - 1+ Ce"where is an arbitrary constant is given by the family of curves 2y=**** where x arbitrary constant º + where x ban arbitrary constant None of them + y = + where Karbary.com + is where is an arbitrary constant
The orthogonal trajectories of the family of curves 22 = 2y - 1+ Ce-24, where is an arbitrary constant, is given by the family of curves None of them * + y2 + k where k is an arbitrary constant 4 24 xy? + k where k is an arbitrary constant 4 x+y= + k where k is an arbitrary constant 4 O 2? + y 24 4 + k where K is an arbitrary constant
Consider the partial differential equation, with the initial condition: 1 2yuz + 3x?uy = 9x?y?, u(x,0) = x3 + 1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
Consider the partial differential equation, with the initial condition: 1 2 cup +3cºu, = 9x²y?, u(x,0) = x3 +1 Find the characteristic curves and the orthogonal trajectories and sketch both on the same graph. Find a solution of the partial differential equation with the given initial con- dition valid in the first quadrant of the (x, y)-plane. Is this solution unique? Explain.
Question 3 The orthogonal trajectories of the family of curves go? = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves + kwhere is an arbitrary constant o 2 + y2 + k where K is an arbitrary constant 4 None of them C zy +k where x is an arbitrary constant 4 24 2 + y = + k, where k is an arbitrary constant 4
please show work
3 pts Question 3 The orthogonal trajectories of the family of curves ? = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves way + where k is an arbitrary constant 4 x + + where K is an arbitrary constant 4 None of them 2y + where K is an arbitrary constant 4 o 22 + y = + k, where k is an arbitrary constant 4.
Question 3 3 pts The orthogonal trajectories of the family of curves x2 = 2y - 1+ Ce-2y, where is an arbitrary constant, is given by the family of curves None of them 2 + y2 Alt + k where k is an arbitrary constant 4 xy? + k, where k is an arbitrary constant 4 O x? y + k where k is an arbitrary constant 4 x2 + y = + k, where K is an arbitrary constant...
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate the gradient of f at the point (1,2). c) Find a direction (expressed as a unit vector) for which the directional derivative at the point (1,2) is 0.
13) Consider the function f(, y)-4x2 +y a) Sketch a graph of level curves for fox.y)-4,8 and 16 (they should be ellipses) in xa-plare b) Calculate...
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1. Consider the family of curves y = 22 + c family of orthogonal trajectories. Sketch some curves from both families on the same graph. 3. A tank starts with 10 L tank at a rate of 1 L/min. Th ow long it takes for Thin. The well-stirred m with 10 L of water into which 20 g of salt is poured. Pure water flows into the ta rate of 1 L/min. The well-stirred mixture flows out at...
1. Given: the ellipse with equation 4x2 9y2 36 Use methods of calculus to find each of the following, that is, set up an expression involving a definite integral. Evaluate using a calculator unless otherwise stated. a) Find the area of the ellipse, to three decimal places (10) b) Express the equation of the ellipse in polar form and find its area, to three decimal places. (10) c) The area of an ellipse can be found by using the formula...
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