Show that the equation x (1-x) y (x) + (1 - 5x) y (x) - 4y(x)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Show that the equation x (1-x) y (x) + (1 - 5x) y (x) - 4y(x) = 0 has the following linearly independent solutions: y (x) = [ (1+n) x n n=0 too Y(x) = y(x)lu (x1 - 2 n(n+1)x" n=1 Show that the equation (x + x) y " (x) - (x+x) y'(x) + y(x) = 0 has the following lincarly independent solections: y (x) = x (1+x) , 1 Y(x) = y (x) lu|x1 + 1x1 | -2x - 2 --jh y, n=2 n(n-1) X Show that the equation x (1-x) y (x) + (1 - 5x) y (x) - 4y(x) = 0 has the following linearly independent solutions: y (x) = [ (1+n) x n n=0 too Y(x) = y(x)lu (x1 - 2 n(n+1)x" n=1 Show that the equation (x + x) y " (x) - (x+x) y'(x) + y(x) = 0 has the following lincarly independent solections: y (x) = x (1+x) , 1 Y(x) = y (x) lu|x1 + 1x1 | -2x - 2 --jh y, n=2 n(n-1) X
Expert Answer:
Answer rating: 100% (QA)
To show that the differential equation x1xyx 15xyx 4yx 0 has the solutions yx 1nxn and yx yxlnx12nn1 ... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Show that the equation 2x 1 sin x = 0 has exactly one real root.
-
The FL Crime data file on the text CD has data for the 67 counties in Florida on y = crime rate: Annual number of crimes in county per 1000 population x1 = education: Percentage of adults in county...
-
Show that the equation 1 + 2x + x3 + 4x5 = 0 has exactly one real root.
-
The number of hours of daylight that occur at any location on Earth depends on the time of year and the latitude of the location. The equations below model the numbers of hours of daylight in Seward,...
-
The capacitors in Figure are initially uncharged. The capacitances are C1 = 4.0F, C2 = 8.0F, and C3 = 12F, and the battery's potential difference is V = 12V When switch S is closed, how many...
-
\(k_{1}, k_{2}, k_{3}\), and \(k_{4}\) are in series a. \(16,007.75 \mathrm{~N} / \mathrm{m}\) b. \(52,500 \mathrm{~N} / \mathrm{m}\) c. \(64,500 \mathrm{~N} / \mathrm{m}\) d. \(3310.078 \mathrm{~N}...
-
Figure 1-2 shows that developments in IT affect both an organizations strategy and the design of its AIS. How can a company determine whether it is spending too much, too little, or just enough on...
-
During 2011, Lacee Enterprises had gross sales of $247,000. At the end of 2011, Lacee had accounts receivable of $83,000 and a credit balance of $5,600 in Allowance for Bad Debts. Lacee has used the...
-
Calculate the AE given a project with an outlay of -2000 and cash flows of 1500 per year for 4 years. The discount rate is 0.12. The rate is given as a decimal (eg .12 is 12%). Answer to the nearest...
-
A model for the surface area of some solid object is given by S = 0.171uw0.683 h0.439, where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. If the errors...
-
The concrete I-beam of figure below is pre-stressed with four stranded cables having total area Ap=0.575 sq. in. Eccentricity of the steel varies para-bolically from 0 at the supports to 7.58 in at...
-
Expand and simplify. (7y3+ 3)
-
Alisha Incorporated manufactures medical stents for use in heart bypass surgery. Based on past experience, Alisha has found that its total maintenance costs can be represented by the following...
-
Onslow Company purchased a used machine for $288,000 cash on January 2. On January 3. Onslow paid $8,000 to wire electricity to the machine. Onslow paid an additional $1,600 on January 4 to secure...
-
Gable Company uses three activity cost pools. Each pool has a cost driver. Information for Gable Company follows: Activity Cost Pools Machining Designing costs Setup costs Total Cost of Pool Cost...
-
A borrower takes out a 30-year mortgage loan for $100,000 with an interest rate of 6% plus 4 points. What is the effective annual interest rate on the loan if the loan is carried for all 30 years?
-
Island Novelties, Incorporated, of Palau makes two products-Hawaiian Fantasy and Tahitian Joy. Each product's selling price, variable expense per unit and annual sales volume are as follows: Hawaiian...
-
Suppose a population of bacteria doubles every hour, but that 1.0 x 106 individuals are removed before reproduction to be converted into valuable biological by-products. Suppose the population begins...
-
A certain amount of work is required to stretch a spring from its equilibrium position. (a) If twice the work is performed on the spring, the spring will stretch more by a factor of (1) 2 (2) 2, (3)...
-
The drift speed of electrons in a complete circuit, is typically a few millimeters per second. Yet a lamp 3.0 m away from a light switch turns on instantaneously when you flip the switch. Explain...
-
The acceleration due to gravity near a planets surface is known to be . If the escape speed from the planet is 8.42 m/s, (a) Determine its radius. (b) Find the mass of the planet. (c) If a probe is...
-
Can unions increase productivity?
-
What is the impact of unions on wages?
-
How is the price of land determined?
Study smarter with the SolutionInn App