Question

P 6. (6 pts) Mark each statement as True or False. A. “Suppose that yp is...

P 6. (6 pts) Mark each statement as True or False.

A. “Suppose that yp is a particular solution of the ODE a2(x)y′′ + a1(x)y′ + a0(x)y =g(x). Then 3yp is another particular solution of the ODE.”

B. “Suppose that y1 is a solution of the ODE a2 (x)y′′ +a1(x)y′ +a0(x)y= 0. Then 3y1 is another solution of the ODE.”

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

First statement is false because the give question is non homogeneous if we uses the 3y1 as a particular solution that will lead to a multiple factor of 3 in LHS which won't be equal to g(x ) in RHS as it was for y1.

2nd statement is true because that 3y1 factor will go under zero in RHS. As it is a homogeneous equation the constant factor multiple won't change the solution it independent of constant factor even 5 y1 would be a solution for this ODE.

If u still have any doubts plz ask in comment section. Thank you ?

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
Choose “True” or “False” for each statement (10 pts) just answer as true or false a)...
Choose “True” or “False” for each statement (10 pts) just answer as true or false a) True or False: Government intervention is not always necessary to solve negative externalities problems. b) True or False: If there are negative externalities associated with good X, the price of X that a firm charge will be too high compared with socially optimal level of price. c) True or False: If emissions are controlled by tradable pollution permits, total abatement costs are minimized.
Mark the following as true or false, as the case may be. If a statement is...
Mark the following as true or false, as the case may be. If a statement is true, then prove it. If a statement is false, then provide a counter-example. a) A set containing a single vector is linearly independent b) The set of vectors {v, kv} is linearly dependent for every scalar k c) every linearly dependent set contains the zero vector d) The functions f1 and f2 are linearly dependent is there is a real number x, so that...
7. Answer the following questions true or false and provide an explanation. • If you think...
7. Answer the following questions true or false and provide an explanation. • If you think the statement is true, refer to a definition or theorem. • If false, give a counter-example to show that the statement is not true for all cases. (a) Let A be a 3 × 4 matrix. If A has a pivot on every row then the equation Ax = b has a unique solution for all b in R^3 . (b) If the augmented...
True/False. If false, correct the statement. 2 pts each= 16 pts 1. In comparison to other...
True/False. If false, correct the statement. 2 pts each= 16 pts 1. In comparison to other countries such as France and Japan, the United States has a relatively low national infant mortality rate. a. b. If false, correct the statement: 2. Maternal mortality is the measure of a nation’s health. a. b. If false, correct the statement: 3. From 1982 through 2006, there has been no decline in deaths from pregnancy-related complications. a. b. If false, correct the statement: 4....
1. For each statement that is true, give a proof and for each false statement, give...
1. For each statement that is true, give a proof and for each false statement, give a counterexample     (a) For all natural numbers n, n2 +n + 17 is prime.     (b) p Þ q and ~ p Þ ~ q are NOT logically equivalent.     (c) For every real number x ³ 1, x2£ x3.     (d) No rational number x satisfies x^4+ 1/x -(x+1)^(1/2)=0.     (e) There do not exist irrational numbers x and y such that...
6) (8 pts, 4 pts each) State the order of each ODE, then classify each of...
6) (8 pts, 4 pts each) State the order of each ODE, then classify each of them as linear/nonlinear, homogeneous/inhomogeneous, and autonomous/nonautonomous. A) Unforced Pendulum: θ′′ + γ θ′ + ω^2sin θ = 0 B) Simple RLC Circuit with a 9V Battery: Lq′′ + Rq′ +(1/c)q = 9 7) (8 pts) Find all critical points for the given DE, draw a phase line for the system, then state the stability of each critical point. Logistic Equation: y′ = ry(1 −...
Python questions 1) Mark true or false according to the following functions below. a) f(x) =...
Python questions 1) Mark true or false according to the following functions below. a) f(x) = a1 + a2x + a3x^2 is linear in x b) f(x) = a1 + a2x + a3x^2 is linear in the ai for i = 1, 2, 3 c)  f(x, y) = x log(y) is linear in x d)  f(x, y) = x log(y) is linear in y 2) What order does the interpolating polynomial through 6 points have? 3) For this problem, you have measured...
(a) Let the statement, ∀x∈R,∃y∈R G(x,y), be true for predicate G(x,y). For each of the following...
(a) Let the statement, ∀x∈R,∃y∈R G(x,y), be true for predicate G(x,y). For each of the following statements, decide if the statement is certainly true, certainly false,or possibly true, and justify your solution. 1 (i) G(3,4) (ii) ∀x∈RG(x,3) (iii) ∃y G(3,y) (iv) ∀y¬G(3,y)(v)∃x G(x,4)
MARK TRUE OR FALSE FOR EACH STATEMENT 1. The total population contributes to the denominator of...
MARK TRUE OR FALSE FOR EACH STATEMENT 1. The total population contributes to the denominator of incidence measures 2. A report of a clinical trial of a new drug versus a placebo noted that the new drug gave a higher proportion of successes than did the placebo (70% versus 40%). The report ended with the statement that the p value associated with this finding was equal to 0.05. This means that 5 out of 100 patients did not benefit from...
Determine whether each statement is true or false. If the statement is false, give an example...
Determine whether each statement is true or false. If the statement is false, give an example showing that it is false in general. a) If events A_1, A_2, A_3 partition a sample space, then the events A_1 and A_2 are independent. b) If events A_1, A_2, A_3 partition a sample space, then the events A_1, A_2 are disjoint. c) If the events A_1, A_2, A_3 are pairwise independent events, then A_1, A_2, A_3 are mutually independent events. d) For any...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT