Differential Equations (4) Find the Wronskian of the following sets of solutions. Do the solutions form...
For the differential equation in) pin -1) + ... + Polly with solutions ....Yo Abel's formula for the Wronskian is Wy ... (t) = cel ot Consider the equation (4) - y 0 . (a) Use Abel's formula from above to find the Wronskian of a fundamental set of solutions of the given equation. (Use as the constant mentioned in Abel's formula.) w(t) ce el cost, and sint. (b) Determine the Wronskian of the solutions d Wel, e, cost, sin...
Differential equation 1. Chapter 4 covers differential equations of the form an(x)y("4a-,(x)ye-i) + +4(x)y'+4(x)-g(x) Subject to initial conditions y)oyy-Co) Consider the second order differential equation 2x2y" + 5xy, + y-r-x 2- The Existence of a Unique Solution Theorem says there will be a unique solution y(x) to the initial-value problem at x=而over any interval 1 for which the coefficient functions, ai (x) (0 S is n) and g(x) are continuous and a, (x)0. Are there any values of x for...
Differential equations / which pair of functions below cannot be a fundrmental set of solutions? 6. Which pair of functions below cannot be a fundamental set of solutions? (8 Points) 1, x3, xinx 3 cost + 6 sint, 5 cost + 10 sint €2x cos 3x + sin 3x, 1 e-31 3 te-31 5et + 5, 2e + 1
1. Compute the Wronskian for the following functions. Then use the Wronskian to determine whether the functions are linearly independant or linearly dependant. a) {(tan2x - sec2 x),3 (b) le,e,e) 2. Use variation of parameters to find a general solution to 2y" -4ry 6y3 1 given that y 2 and y2- 3 are linearly independant solutions of the associated homogeneous equation. (Hint: be careful the equations are in the right form.) Find a particular solution for each of the following...
1. (20 pts.) In the following Problems: (a) Seek power series solutions of the given differential equation about the given point xo ; find the recurrence relation. (b) Find the first four terms in each of two solutions yi and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W(y1, y2)(xo), show that yı and y2 form a fundamental set of solutions. (d) If possible, find the general term in each solution. i) y" +k+x+y = 0, 40...
Find the Wronskian of two solutions of the given differential equation without solving the equation. 9. x'y'+xy(2-y 0, Bessel's equation 10. (I-x)y"-2xy+a(a+y-0, Legendre's equation
In each of Problems 3 and 4 (a) Seek the power series solutions of the given differential equation about the given point ro: find the recurrence relation. (b) Find the first four terms in each of two solutions vi and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W (, 2)(o), sow that n and y2 form a fundamental set of solutions (d) If possible, find the general term in each solution. 3. Exercise 5.2 #5. 4....
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential equation on the interval (-oo, oo) Find the Wronskian of y1,3/2 (Note the order matters) Do the functions y1, 32 form a fundamental set on -oo, 0o)? Answer should be yes or no
Find the Wronskian of two solutions (up to a constant multiple) to the differential equation without solving the equation: (1 - 2?)y" - 2xy + 2y = 0 (this is a well-known equation called Legendre's equation. Its solutions are called Legendre functions). Impossible to determine from the given information O where c is a constant 1-22 O ce 1-22 where c is a constant O cln |1 - 22 where c is a constant
Differential Equations. Can someone show a more detailed solution? Having a bit of trouble understanding how to get there with the provided solution. 8. Assume that Xi (t) = (t, 1)T and X2(t) = (t2, 2t)" are solutions of a 2x 2 linear system X, P (t) X of differential equations. The Wronskian of Xi and X2 equals t showing that Xi and X2 form a fundamental set of solutions on interval(s) o,0)U(0,00) There is a unique solution of X...