differential equation a. Show that y = y2 + y2 is a solution of y" +...
Need the answer as soon as possible a. Show that y = y + y2 is a solution of y" + P(x)y' + Q(x)y = T (x) + T2(x) if y, and y, are the solution of the following equations respectively; y + P(x)y' + Q(x)y = Ti(x) and y" + P(x)y' + Q(x)y = T2(x) (CO2:P01 - 4 Marks) b. Determine the general solution of the given equation using method of undetermined coefficients y" +9y = 2 sin 3x...
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
please give me whole solution for this question x2 y2 satisfies the differential equation Show that z = (x2+y2) az az y X дх 2z а. ay
Solve differential equation y'=x?y2 by separation of variables, it has a general solution -- Select the correct answer. a. y = b. y = 3 c. y=- x+c d. y = y2 + 2xy + c 2 e. y = x²+c
y'' = x + y2 + y' y(0) = 1, y(1) = 0 calculate the differential equation using h = 1/3 with difference equations, it is enough to calculate y(1/3) and y(2/3).
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
Find the general solution of the differential equation xy' = y + (x2 + y2 y(4) = 3
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...
Show that there are no solutions to the equation p+ q2 = y2 + y2 + t2 where p, q, r, s, t are primes. (Hint: Consider the remainder of the square of an odd integer when divided by 8, and then consider cases.]
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...