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1-14 ODES. INTEGRATING FACTORS Test for exactness. If exact, solve. If not, use...
solution for all 4 please In Problems 1-3, solve the given DE or IVP (Initial-Value Problem)....
solution for all 4 please
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is. 1. (2xy + cos y) dx + (x2 – x sin y – 2y) dy = 0. 1 dy 2. + cos2 - 2.cy y(y + sin x), y(0) = 1. + y2 dc 3. [2xy cos (2²y) – sin x) dx + x2 cos (x²y) dy = 0. (1+y! x" y® is...
(4) Solve for y using Integrating Factors. [15 Points] y' + y = x2 (5) Solve...
(4) Solve for y using Integrating Factors. [15 Points] y' + y = x2 (5) Solve for y by first showing that equation is Exact and then solving it using Exact Differential Equation. [15 Points] [sin y + ycosx]dx + [sin x + xcofy]dy = 0 (6) Solve for y by the separable equation. [15 Points] sin(2x)dx + cos(3y)dy = 0 when y 5) =
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
Select all of the exact ODEs listed below. (3x3y2 + 3) dx + (2x3y – 2)...
Select all of the exact ODEs listed below. (3x3y2 + 3) dx + (2x3y – 2) dy = 0 (4 sin(4x) (x - y) + cos(4x)) dx - cos(4x)dy = 0 (4 cos(4x) (x - y) + sin(4x) dx - sin(4x)dy = 0 (3x2y2 + 3) dx + (2xy3 – 2) dy = 0 +
2. Solve the following set of homogeneous first-order ODEs using the substitution y = vx. (a)...
2. Solve the following set of homogeneous first-order ODEs using the substitution y = vx. (a) 2xy = 3(x2 + y²), given y = 2 when x = 1. (b) x = y(In x – Iny), given y = 4 when x = 1. (C) (x2 + 3xy + y2). dx - x2.dy = 0, given y = 0 when x = 1.
Name: ID number:_ Q1. Test for exactness. If exact solve the ODE or the IVP. If...
Name: ID number:_ Q1. Test for exactness. If exact solve the ODE or the IVP. If not find an integrating factor, then solve. b. (x2 + y*)dx-2xdy = 0, y(1) = 0.
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3....
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points)...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points) (2x + tan y) dx + (x - x2 tan y) dy = 0 O u = csc y O u = - tan y O u = cos y O u = sec y This question is required.
In Problems 5-6, determine an Integrating Factor for the given DE. 5. [2x + (x2 +...
In Problems 5-6, determine an Integrating Factor for the given DE. 5. [2x + (x2 + y2) cot x]dx + 2ydy = 0. 6. + (+ 1)dy = 0. 7. Use Euler's Method with the specified Step Size (h), to determine the solution to the given IVP at the specified point. y = x2 + y², y(1) = 2, h = 0.2; y(1.4)~?
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ;...
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
solution for all 4 please
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is. 1. (2xy + cos y) dx + (x2 – x sin y – 2y) dy = 0. 1 dy 2. + cos2 - 2.cy y(y + sin x), y(0) = 1. + y2 dc 3. [2xy cos (2²y) – sin x) dx + x2 cos (x²y) dy = 0. (1+y! x" y® is...
(4) Solve for y using Integrating Factors. [15 Points] y' + y = x2 (5) Solve for y by first showing that equation is Exact and then solving it using Exact Differential Equation. [15 Points] [sin y + ycosx]dx + [sin x + xcofy]dy = 0 (6) Solve for y by the separable equation. [15 Points] sin(2x)dx + cos(3y)dy = 0 when y 5) =
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
Select all of the exact ODEs listed below. (3x3y2 + 3) dx + (2x3y – 2) dy = 0 (4 sin(4x) (x - y) + cos(4x)) dx - cos(4x)dy = 0 (4 cos(4x) (x - y) + sin(4x) dx - sin(4x)dy = 0 (3x2y2 + 3) dx + (2xy3 – 2) dy = 0 +
2. Solve the following set of homogeneous first-order ODEs using the substitution y = vx. (a) 2xy = 3(x2 + y²), given y = 2 when x = 1. (b) x = y(In x – Iny), given y = 4 when x = 1. (C) (x2 + 3xy + y2). dx - x2.dy = 0, given y = 0 when x = 1.
Name: ID number:_ Q1. Test for exactness. If exact solve the ODE or the IVP. If not find an integrating factor, then solve. b. (x2 + y*)dx-2xdy = 0, y(1) = 0.
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points) (2x + tan y) dx + (x - x2 tan y) dy = 0 O u = csc y O u = - tan y O u = cos y O u = sec y This question is required.
In Problems 5-6, determine an Integrating Factor for the given DE. 5. [2x + (x2 + y2) cot x]dx + 2ydy = 0. 6. + (+ 1)dy = 0. 7. Use Euler's Method with the specified Step Size (h), to determine the solution to the given IVP at the specified point. y = x2 + y², y(1) = 2, h = 0.2; y(1.4)~?
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
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