Homework Answers
Given 
Computing W gives us 
Thus the particular solution is:
Solving this integral, we get the answer 
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Chapter 4, Section 4.7, QUestion 23 Given that the given functions yı and y2 satisfy the...
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a...
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y" – 3xy' + 4y = 7x? In x, x>0; 71(x) = x2, yz(x) = x2 In x Y(x) =
Part A Part B Kindly show the detailed solution for reviewer. Thanks! I'll rate it The...
Part A
Part B
Kindly show the detailed solution for reviewer.
Thanks! I'll rate it
The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution 72(x) of the homogeneous equation and a particular solution Yp(x) of the given nonhomogeneous equation. y" - 3y + 2y = 11e3x, Yu = ex Y2(X) Yo(x) = The indicated function yı(x) is a solution of the given differential equation. Use...
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the fun...
Part A is first 2 lines, Part B is last 2 lines, thanks!
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y2(x) are linearly independent solutions ofthe corresponding homogeneous equation. Note: The cocfficient of y" must always be 1, and hence a preliminary division may be required y2(x) = x-2 ·y1(x) = x y2(x) = ex
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
Chapter 5, Section 5.2, Question 2 In the Problem: • a. Seek power series solutions of...
Chapter 5, Section 5.2, Question 2 In the Problem: • a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. . b. Find the first four nonzero terms in each of two solutions yn and y2 (unless the series terminates sooner). • c. By evaluating the Wronskian W[y1, y2](xo), show that y, and y2 form a fundamental set of solutions. • d. If possible, find the...
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the...
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the homogeneous differential equation corresponding to ty" + t'y" – 2ty' + 2y = 2*, t > 0, use variation of parameters to find its general solution.
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x)...
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x) = x3 are solutions to the corresponding homogeneous differential equation. Be sure to fully evaluate any integrals that arise. (You will have to use polynomial long division.) " - 3xy' + 3y = y(1) = 0, y(1) = 0 1+2
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı...
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı = et and y2 = t+1 are a fundamental set of solutions to the associated homogeneous equation. (b) Find a particular solution using variation of parameters.
The indicated function yı() is a solution of the given differential equation. Use reduction of order...
The indicated function yı() is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, Y2 = vy() / e-SP(x) dx dx (5) y?(x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y1 = x2 Y2 The indicated function yı(x) is a solution of the given differential equation. 6y" + y' - y = 0; Y1 Fet/3 Use reduction of order or formula (5) in Section...
Given that yı(t) =ť is a solution to the ODE: ty' + 4ty – 10y =...
Given that yı(t) =ť is a solution to the ODE: ty' + 4ty – 10y = 0, use the reduction of order method to find another solution y2 corresponding to the initival values ya(1)=- and y(1)= y2(t) =
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y" – 3xy' + 4y = 7x? In x, x>0; 71(x) = x2, yz(x) = x2 In x Y(x) =
Part A
Part B
Kindly show the detailed solution for reviewer.
Thanks! I'll rate it
The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution 72(x) of the homogeneous equation and a particular solution Yp(x) of the given nonhomogeneous equation. y" - 3y + 2y = 11e3x, Yu = ex Y2(X) Yo(x) = The indicated function yı(x) is a solution of the given differential equation. Use...
Part A is first 2 lines, Part B is last 2 lines, thanks!
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y2(x) are linearly independent solutions ofthe corresponding homogeneous equation. Note: The cocfficient of y" must always be 1, and hence a preliminary division may be required y2(x) = x-2 ·y1(x) = x y2(x) = ex
For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
Chapter 5, Section 5.2, Question 2 In the Problem: • a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. . b. Find the first four nonzero terms in each of two solutions yn and y2 (unless the series terminates sooner). • c. By evaluating the Wronskian W[y1, y2](xo), show that y, and y2 form a fundamental set of solutions. • d. If possible, find the...
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the homogeneous differential equation corresponding to ty" + t'y" – 2ty' + 2y = 2*, t > 0, use variation of parameters to find its general solution.
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x) = x3 are solutions to the corresponding homogeneous differential equation. Be sure to fully evaluate any integrals that arise. (You will have to use polynomial long division.) " - 3xy' + 3y = y(1) = 0, y(1) = 0 1+2
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı = et and y2 = t+1 are a fundamental set of solutions to the associated homogeneous equation. (b) Find a particular solution using variation of parameters.
The indicated function yı() is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, Y2 = vy() / e-SP(x) dx dx (5) y?(x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y1 = x2 Y2 The indicated function yı(x) is a solution of the given differential equation. 6y" + y' - y = 0; Y1 Fet/3 Use reduction of order or formula (5) in Section...
Given that yı(t) =ť is a solution to the ODE: ty' + 4ty – 10y = 0, use the reduction of order method to find another solution y2 corresponding to the initival values ya(1)=- and y(1)= y2(t) =
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