Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant-...

Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0.

a) Rewrite the equation as constant- coefficeint equation by substituting x = e^t.

b) Solve it when x(1)=0, x'(1)=1.

Expert Solution

Colby Messinger answered 9 months ago

a) Solve the Cauchy-Euler equation: x^2y'' - xy' + y = x^3 b) Solve the initial-value...

a) Solve the Cauchy-Euler equation: x^2y'' - xy' + y = x^3 b) Solve the initial-value problem: y'' + y = sec^3(x); y(0) = 1, y'(0) =1/2

($4.7 Cauchy-Euler Equations): Solve the following Euler-type equations (a)–(c). (a) x^2y''-4xy'-6y=0 (b) x^2y''+7xy'+13y=0 (c) x^2y''+3xy'+y=x

X^2y''+6xy'+6y=4lnx, cauchy euler

In Exercises 1-20, find a general solution of the Cauchy-Euler equation. (Assume x > 0). (x^(2))y''-5xy'+9y=0

Solve the Cauchy-Euler equation x4y'''' - 4x2y'' + 8xy' - 8y = 12xlnx x > 0

Consider the equation xy′′+y′+y= 0, x >0. a) Verify that 0 is a regular singular point....

Consider the equation xy′′+y′+y= 0, x >0. a) Verify that 0 is a regular singular point. (b) Find the indicial equation and its roots. c) Determine the recurrence relation(you do NOT need to find the solutions).

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...

Question

Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for x>0. a) Rewrite the equation as constant-...

Solutions

Expert Solution

Related Solutions