The functions y1(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation t’y" – 4ty' + 6y = 0 %3! on (0, 0). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous differential equation t*y" – 4ty' + 6y = 4t%, %3D what is the function u(t) ? (Submit the corresponding number without parentheses.)

The functions y1(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation t’y" – 4ty' + 6y = 0 %3! on (0, 0). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous differential equation t*y" – 4ty' + 6y = 4t%, %3D what is the function u(t) ? (Submit the corresponding number without parentheses.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

Q: 5. 320 > 243*

Q: Verify that y =t is a solution to the differential equation %3D ty" – t(t + 2)y' + (t + 2)y = 0, t >…

Q: Let the differential equation be: y" – 6y' + 9y = e3, where the complementary function is: Yc =…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Introduction: The variation of parameter is a very efficient tool that is used to determine the…

Q: d²y dt² +4y= cos2t y(0) = -2 and y'(0) = 0

Q: (c) and Y2(t) 7. The functions Y₁(t) = t and Y₂(t) = tet form a fundamental pair of solutions to the…

Q: A curve that satisfies the differential equation dr dy = y-x passes through the point 0.. (*) (a)…

A: According to Euler's method:y(x+h)≈y(x)+hdydx, given y(0)=12.we need to find y(1)Inorder to find…

Q: Consider the Non-Homogenous differential equation: y" - 2y" - 4y' + 8y 5e +x + 3 Given that y, -…

A: Given that, The complimentary solution is,

Q: Determine the differential equation on which the general solution is y=cos(A+Bx). A (1-y2)y"+yy'=0…

A: Topic = Differential equation

Q: Consider the differential equation y" - y' - 30y = 0. Verify that the functions e-5x and e6x form a…

A: If Wronskian is non zero then solution is linearly independent. Here W(e-5x, e-6x) =11ex since ex

Q: Show that y = x³ – x² +5 (where C is a constant) is a solution of the differential x y" + 2y' =…

A: Differentiating with respect to x, we get

Q: Three linearly independent solutions of the differential equation y "+4y' D0 are Select the correct…

A: We will find out the required solution.

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: Verify that the given two-parameter family of functions is the general solution of the…

Q: Find the differential equation of the general solution y = Ae2x + Bxe²x А. у" — 4y' + 4у %3D0 В. у"…

A: To find the differential equation of the given general solution y=Ae2x+Bxe2x

Q: dy Find the general (real) solution of the differential equation ( y' = Y ): dx y"- 6 y' + 117/4 y=0…

Q: Find the general solution of the following partial differential equation (D2 + 7DD' + 12D'2)z = 17…

Q: The suitable form of the differential equation y" + 2y'-3y = 5e2t, is Y = Aje2t, then the value of…

Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: Consider the differential equation ty" – t(t + 2)y +(t +2)y = 0, t> 0. (4) The function yı(t) = t is…

Q: Use the method of variation of parameters to find a particular solution of the following…

Q: y"- y'=0 ; y, (t) =e y,(1)=e* y= 3t +r a. b. y"+2y'-3y 0 c. ty'-y=r ; y. (1) = cosht y:(1)=d : с.

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The functions yı(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation
%3D
%3D
t’y" – 4ty' + 6y = 0 on (0, ∞).
When using variation of parameters with y = u1(t)t² +U2(t)t³ to find a solution of the nonhomogeneous
differential equation
t²y" – 4ty' + 6y = 4t°,
what is the function u(t) ? (Submit the corresponding number without parentheses.)
(1) 4
(2) –4
(3)
(5) –4t
(6) –4t²

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Explain the determine
Consider the differential equation a2y" + 3ry' - 8y = 0. (a) Verify that the function y1 = x² is a solution of that equation on the interval (0, o0). Problem 4 (b) Using the method of reduction of order, find another solution y2 of that equation on (0, o0) such that yi and y2 are linearly independent. (Hint. Use the formula provided below. Be careful to apply it correctly!) (c) Using part (a) and (b) find the general solution of that equation.
Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y2 are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty" (t+1)y+y=23t²; Y₁ = e², y₂ =1+1 Set up the particular solution yp (t) = v₁ (t)y₁ (t) + v2(t)y2(t) to the nonhomogeneous equation by substituting in two linearly independent solutions (y₁ (t), y2(t)} to the corresponding homogenous equation. Yp(t)= ☐
Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y₂ are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty'' - (t+1)y' + y = 17t²; Y₁ = e¹₁ y₂=t+1 Set up the particular solution y(t) = V₁ (t)y₁ (t) + V₂ (t)y₂ (t) to the nonhomogeneous equation by substituting in two linearly independent solutions (y₁ (t), Y₂(t)} to the corresponding homogenous equation. Y₁ (t) =
The differential equation 3Y = y – y? has one of the following one parameter families as its general solution 1 1+ ce-* 1 y = c+ x? Find the solution such that y(0) = 2:
Which of the following is the solution of the Differential Equation with initial values?(img8) Select one:(img9)
If y, = e' is a solution to the differential equation (t – 1)y" – ty' + y = 0,t > 0 a second linearly dependent solution is : A. y2 = -t B. y2 = 3et C. y2 = t D. y2 = 3tet %3D E. y2 = te
Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d² u fu dx² 2 + - 0, f = f(x). Let w = uz/u₁. Show that w' = c/u for some nonzero constant c. Let y = -2u₁/u₁. Show that y satisfies the Ricatti equation y² V-2-1 y' f.