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(1 point) General Solution of a First Order Linear Differential Equation A first order linear differential...
2. Find the general solution to the first-order linear differential equation dy ex x + 2y...
2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. =- X
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying...
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
(1 point) In this problem we consider an equation in differential form M d.c + N...
(1 point) In this problem we consider an equation in differential form M d.c + N dy=0. The equation (42 +3=”y 2) dx + (422.1, + 3)dy=0 y in differential form ñ dx + Ñ dy=0 is not exact. Indeed, we have Ñ , -Ñ , For this exercise we can find an integrating factor which is a function of y alone since Ñ , - Ñ , M is a function of y alone. Namely we have (y) =...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set...
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set Y2-uz" Then (using the prime notation for the derivatives) So, plugging 32 into the left side of the differential equation, and reducing, we get The reduced form has a common factor of r5 which we can divide out of the equation so that we have ru" + u0 Since this equation does not have any u terms in it we can make the substitution...
In this problem we consider an equation in differential form M dx + N dy =...
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...
both please 1. Use the method of separation of variables find the general (explicit) solution to...
both please
1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy dy 2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx X by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. 0
(1 point) A first order linear equation in the form y' + p(x) = f(x) can...
(1 point) A first order linear equation in the form y' + p(x) = f(x) can be solved by finding an integrating factor (1) exp(/ pla) de) (1) Given the equation ay' + (1 + 2x) y = 8e 22 find (x) (2) Then find an explicit general solution with arbitrary constant C (3) Then solve the initial value problem with y(1) - ?
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp (1) Given the equation y' + 2y = 2 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(0) 2
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp ( (1) Given the equation y, +-= 7x4 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(1) = 2
2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. =- X
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
(1 point) In this problem we consider an equation in differential form M d.c + N dy=0. The equation (42 +3=”y 2) dx + (422.1, + 3)dy=0 y in differential form ñ dx + Ñ dy=0 is not exact. Indeed, we have Ñ , -Ñ , For this exercise we can find an integrating factor which is a function of y alone since Ñ , - Ñ , M is a function of y alone. Namely we have (y) =...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set Y2-uz" Then (using the prime notation for the derivatives) So, plugging 32 into the left side of the differential equation, and reducing, we get The reduced form has a common factor of r5 which we can divide out of the equation so that we have ru" + u0 Since this equation does not have any u terms in it we can make the substitution...
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...
both please
1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy dy 2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx X by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. 0
(1 point) A first order linear equation in the form y' + p(x) = f(x) can be solved by finding an integrating factor (1) exp(/ pla) de) (1) Given the equation ay' + (1 + 2x) y = 8e 22 find (x) (2) Then find an explicit general solution with arbitrary constant C (3) Then solve the initial value problem with y(1) - ?
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp (1) Given the equation y' + 2y = 2 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(0) 2
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor μ(x) = exp ( (1) Given the equation y, +-= 7x4 find μ(x) (2) Then find an explicit general solution with arbitrary constant C p(x) dx (3) Then solve the initial value problem with y(1) = 2
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