Question

This is for Differential Equations. I was sick last week and missed class so I do...

This is for Differential Equations. I was sick last week and missed class so I do not understand the process behind solving this question.

Problem 3 Consider the ODE t 2 y'' + 3 t y' + y = 0.

• Factorize the left hand side of the ODE. Hint: One of the factors is (D + 2 t -1 I).

• Find the fundamental set of solutions.

• Solve the initial value problem t 2 y'' + 3 t y' + y = 0, y (1) = 1, y' (1) = 0

Any help would be greatly appreciated, I am especially confused about the factorization part. Please show all steps and work I need to understand the process behind each problem. Thanks in advance!

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty =...
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty = t Solve the ODE 3. ty' - y = t^3 e^(3t), for t > 0 Compare the number of solutions of the following three initial value problems for the previous ODE 4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0 Solve the IVP, and find the interval of validity of the solution 5. y' + (cot x)y = 5e^(cos x),...
This is a differential equations problem: use variation of parameters to find the general solution to...
This is a differential equations problem: use variation of parameters to find the general solution to the differential equation given that y_1 and y_2 are linearly independent solutions to the corresponding homogeneous equation for t>0. ty"-(t+1)y'+y=18t^3 ,y_1=e^t ,y_2=(t+1) it said the answer to this was C_1e^t + C_2(t+1) - 18t^2(3/2+1/2t) I don't understand how to get this answer at all
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...
I had asked this question last week: State whether or not the following equations are autonomous...
I had asked this question last week: State whether or not the following equations are autonomous and identify all equilibrium solutions (if any): y' = t-1. Clearly it is not autonomous. The book says that it has no equilibrium solutions, isoclines are t=constant. However, in Chegg, the same question has been answered saying that t=1 is an equilibrium solution. Please clarify this discrepancy. Someone answered by showing some steps and then concluded, therefore, t=1 is an equilibrium solution for equation...
Consider the differential equation L[y] = y′′ + p(t)y′ + q(t)y = f(t) + g(t), and...
Consider the differential equation L[y] = y′′ + p(t)y′ + q(t)y = f(t) + g(t), and suppose L[yf] = f(t) and L[yg] = g(t). Explain why yp = yf + yg is a solution to L[y] = f + g. Suppose y and y ̃ are both solutions to L[y] = f + g, and suppose {y1, y2} is a fundamental set of solutions to the homogeneous equation L[y] = 0. Explain why y = C1y1 + C2y2 + yf...
Hello! I hope you are healthy and well! I am hoping that this message finds you...
Hello! I hope you are healthy and well! I am hoping that this message finds you happy and content! I am having trouble solving this 5-part practice problem. I would greatly appreciate any and all help that you could lend! Thanks in advance! Given that A and B are true and X and Y are false, determine the truth values of the propositions in the following problem: ∼[(B • ∼X) ⊃ ∼(Y • ∼B)] ⊃ [∼(X ⊃ A) ∨ (B...
: Find solution to the following differential equations, t as independent variable I. u''+ 19211 =...
: Find solution to the following differential equations, t as independent variable I. u''+ 19211 = 0 u(0) = 1/ 6 u'(0) =-1 2. u'+0.125u'+u 0 u(0)2 '(0) 0 3.+1,000,0000 0 Q(0) = 0.13 x 10-6 and Q (0)
DIFFERENTIAL EQUATIONS PROBLEM Consider a population model that is a generalization of the exponential model for...
DIFFERENTIAL EQUATIONS PROBLEM Consider a population model that is a generalization of the exponential model for population growth (dy/dt = ky). In the new model, the constant growth rate k is replaced by a growth rate r(1 - y/K). Note that the growth rate decreases linearly as the population increases. We then obtain the logistic growth model for population growth given by dy/dt = r(1-y/K)y. Here K is the max sustainable size of the population and is called the carrying...
Hello! I hope you are healthy and well! I am hoping that this message finds you...
Hello! I hope you are healthy and well! I am hoping that this message finds you happy and content! I am having trouble solving this 5-part practice problem. I would greatly appreciate any and all help that you could lend! Thanks in advance! In the following proof, what is the justification for line 7? 1.     [(W ⊃ X) ⊃ Y] ∨ ( P ≡ Q) 2.     ∼X • ∼Y 3.     ∼(P ≡ Q) / ∴ ∼W 4.     ∼X                  2 Simp 5.     ∼Y                  2 Simp 6.     (W ⊃ X)...
Use C++ in Solving Ordinary Differential Equations using a Fourth-Order Runge-Kutta of Your Own Creation Assignment:...
Use C++ in Solving Ordinary Differential Equations using a Fourth-Order Runge-Kutta of Your Own Creation Assignment: Design and construct a computer program in C++ that will illustrate the use of a fourth-order explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients of a fourth-order Runge-Kutta method.   See the Mathematica notebook on solving the equations for 4th order RK method.   That notebook can be found at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT