Apply Theorems 5 and 6 to find general solutions of the differential equations given in Problems 33
Question:
Apply Theorems 5 and 6 to find general solutions of the differential equations given in Problems 33 through 42. Primes denote derivatives with respect to x.
2y'' + 3y' = 0
Transcribed Image Text:
THEOREM 5 Distinct Real Roots If the roots ₁ and 2 of the characteristic equation in (18) are real and distinct, then y(x) = c₁e¹¹x + c₂e¹2x (19) is a general solution of Eq. (16). Thus the solution space of the equation ay" + by' + cy = 0 has basis {ex, e¹2x}.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (2 reviews)
0iy...View the full answer
Answered By
Robert Mwendwa Nzinga
I am a professional accountant with diverse skills in different fields. I am a great academic writer and article writer. I also possess skills in website development and app development. I have over the years amassed skills in project writing, business planning, human resource administration and tutoring in all business related courses.
4.90+
187+ Reviews
378+ Question Solved
Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
Question Posted:
Students also viewed these Mathematics questions
-
In Problems 4366, find the real solutions, if any, of each equation. Use the quadratic formula. 4 + X 1 X = 0
-
Li Jun, an office administrator, is evaluating the following quotation that she received for the purchase of a printer for her office: Lease Option: Make payments of $85 at the beginning of every...
-
Determine the dimensions of Nul A, Col A, and Row A for the matrices. A = 0 0 4 7 0 0 0
-
Describe how price variances create incentives to build inventories.
-
What is a lean producer?
-
Lucy, from Problem 4, spends all her income on lemonade, which costs $1 per pint. She earns $300 per month, but is robbed with 25 percent probability, in which case she is left with only $100. She...
-
The speed of turbine and discharge through turbine are proportional to: (a) Head, \(\mathrm{H}\) (b) \(\sqrt{\mathrm{H}}\) (c) \(\mathrm{H}^{2}\) (d) \(\mathrm{H}^{3 / 2}\)
-
A large company is considering cutting back on its TV advertising in favor of business videos to be given to its customers. This action is being considered after the company president read a recent...
-
i need help with this question with an explanation thanks! 7) Large Co. pays its employees $20,000 gross salary each week. 30% of salary is withheld for income taxes and 5% is withheld to pay Social...
-
In Problems 33 through 36, one solution of the differential equation is given. Find the general solution. 9y (3) + 11y" + 4y' - 14y = 0; y = e - x sin x
-
Problems 43 through 47 pertain to the solution of differential equations with complex coefficients. (a) Use Euler's formula to show that every complex number can be written in the form re i , where r...
-
Perform the indicated multiplications. 3(3 2T)(3T + 2)
-
In a car crash, large accelerations of the head can lead to severe injuries or even death. A driver can probably survive an acceleration of 50g that lasts for less than 30 ms, but in a crash with a...
-
Carla holds a ball 1.5 m above the ground. Daniel, leaning out of a car window, also holds a ball 1.5 m above the ground. Daniel drives past Carla at 40 mph and, just as he passes her, both release...
-
Jenny and Alyssa are members of the cross-country team. On a training run, Jenny starts off and runs at a constant 3.8 m/s. Alyssa starts 15 s later and runs at a constant 4.0 m/s. At what time after...
-
Scientists have investigated how quickly hoverflies start beating their wings when dropped both in complete darkness and in a lighted environment. Starting from rest, the insects were dropped from...
-
Loretta agrees to lend Ted $500,000 to buy computers for his consulting firm. They agree to a nominal interest rate of 8%. Both expect the inflation rate to be 2%. a. Calculate the expected real...
-
Repeat the procedure in Exercise 65 for the titration of 25.0 mL of 0.100 M propanoic acid (HC3H5O2, Ka = 1.3 10-5) with 0.100 M KOH.
-
In the synthesis of the keto acid just given, the dicarboxylic acid decarboxylates in a specific way; it gives Explain. HO rather than HO
-
Use the data described in the previous exercise to answer the following questions: a. Investigate your answer to 3.CE.8, part (b), by using the Theory-Based Inference applet to test the following...
-
The Harris polling organization conducted a national survey in 2008, finding that 14% of the sample of 2,302 American adults had a tattoo. a. Use the Theory-Based Inference applet to determine a 99%...
-
A national survey of 47,000 American households in 2006 found that 32.4% of the households included a pet cat. Th is survey result was reported in the 2011 Statistical Abstract of the United States,...
-
8. Define system : (x = A + U (y = Cx 2: systems: (1) Depict the relationships betweenA, B, C and (x = Ax2 + BU , 2 are duality = Cx2 A2, B2, C (2) Prove that the transfer function matrices of and...
-
In September 2022, Alex moved from one Canadian city to another, 500 km away from home to go to college. His moving expenses were $1,450. He spends a lot of time studying and earns good grades, but...
-
What would your NPV be if your cash flow was $381,250 and the discount is 12%?
Study smarter with the SolutionInn App