3. Solve the equation 
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3. Solve the equation knowing that a solution of the corresponding homogeneous equation has the form of a polynomial....
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y =...
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y = 21x + 48, x > 0 Then the general solution to the non-homogeneous equation can be written in the form y(x) = Ax4 + Bx" + Yp. Use reduction of order to find the general solution in this form (your answer will involve A, B, and x) y(x) = Preview
Solve both 3+4 please 3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0. 3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
Solve both 3+4 please
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
2. Using substitution to simplify a problem (a) Solve the following (homogeneous) differential equation using the...
2. Using substitution to simplify a problem (a) Solve the following (homogeneous) differential equation using the appropriate substitution. (b) Find the solution to the equation T+3 Hint: The same substitution wil no longer work, but the equation is almost homogeneous. Use a substitution of the form r- X - h, y-Y - k to reduce this problem to the problem solved in part (a), i.e. choose h and k so that this problem becomes homogeneous in the substituted variables X...
Solve the following differential equation. Do not use Laplace. y'' – 4y' = 2e (2x+3) -...
Solve the following differential equation. Do not use Laplace. y'' – 4y' = 2e (2x+3) - Write the corresponding homogeneous equation and find the homogeneous solution. - Find the particular solution using the non-homogeneous differential equation. - Finally write the general solution.
1. Determine if the differential equation x^2y′=y(x+y) is homogeneous or Bernouilli or both. Give a solution...
1. Determine if the differential equation x^2y′=y(x+y) is homogeneous or Bernouilli or both. Give a solution using any method that applies. 2. Solve the differential equation y′= 2x(y+y^2) using the method of Bernouilli equation. Also give a solution for the same differential equation using the method of separable DE. 3. Consider the differential equation y′′= (y′)^2. It is has both x and y variable missing.Give solutions to the DE using the two different methods corresponding t ox-variable missing, and y-variable...
#8 show all work Problems to be turned in: Solve the following non-homogeneous DEs by the...
#8 show all work
Problems to be turned in: Solve the following non-homogeneous DEs by the Method of Undetermined Coefficients. If initial conditions are given, then obtain the unique solution. 434T-11: O Answer: y(1)--4十8 Answer: y(Ζ)--13 + 19 e2z-2X2-37-8, 0 a 3. y" +4y 3sin(2a) 6. y" +6y+18y 3 cos(3z) - sin(3z) O Answer: O Answer Solve for the complementary solution of the following DEs, and state an appropriate form of the particular solution. DO NOT solve for the undetermined...
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation...
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution ур of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp (a) (10 points) y" – 9y' – 22 y = 5xe -2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation...
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution y, of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp: (a) (10 points) y" - 9y' - 22y = 5xe-2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y =...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos...
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...
Given yı(x) = x4 satisfies the corresponding homogeneous equation of x+y" + 3xy' – 24y = 21x + 48, x > 0 Then the general solution to the non-homogeneous equation can be written in the form y(x) = Ax4 + Bx" + Yp. Use reduction of order to find the general solution in this form (your answer will involve A, B, and x) y(x) = Preview
Solve both 3+4 please
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
2. Using substitution to simplify a problem (a) Solve the following (homogeneous) differential equation using the appropriate substitution. (b) Find the solution to the equation T+3 Hint: The same substitution wil no longer work, but the equation is almost homogeneous. Use a substitution of the form r- X - h, y-Y - k to reduce this problem to the problem solved in part (a), i.e. choose h and k so that this problem becomes homogeneous in the substituted variables X...
Solve the following differential equation. Do not use Laplace. y'' – 4y' = 2e (2x+3) - Write the corresponding homogeneous equation and find the homogeneous solution. - Find the particular solution using the non-homogeneous differential equation. - Finally write the general solution.
#8 show all work
Problems to be turned in: Solve the following non-homogeneous DEs by the Method of Undetermined Coefficients. If initial conditions are given, then obtain the unique solution. 434T-11: O Answer: y(1)--4十8 Answer: y(Ζ)--13 + 19 e2z-2X2-37-8, 0 a 3. y" +4y 3sin(2a) 6. y" +6y+18y 3 cos(3z) - sin(3z) O Answer: O Answer Solve for the complementary solution of the following DEs, and state an appropriate form of the particular solution. DO NOT solve for the undetermined...
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution ур of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp (a) (10 points) y" – 9y' – 22 y = 5xe -2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution y, of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp: (a) (10 points) y" - 9y' - 22y = 5xe-2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...
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