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

Expert Solution

Colby Messinger answered 2 years ago

($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

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

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.

Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation...

Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy/dt and ypp for d2y/dt2.) x2y'' − 3xy' + 13y = 2 + 3x

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

Solve the system of equations: x+y^2=6y x-2y=-5

find the general solution of the equation using cauchy euler. show complete solution x^2 y" -...

find the general solution of the equation using cauchy euler. show complete solution x^2 y" - 3xy' + 3y = 2x^4 e^x

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

Find the solution of the Cauchy problem for the differential equationy" + 2y' + y =...

Find the solution of the Cauchy problem for the differential equationy" + 2y' + y = e–x cos x subject to the initial conditions: y(0) = 0, y'(0) = 1. Verify the solution obtained by direct substitution into the equation and confirm that it satisfies the initial condition.

For the following Cauchy-Euler equation, find two solutions of the homogeneous equation and then use variation...

For the following Cauchy-Euler equation, find two solutions of the homogeneous equation and then use variation of parameters to find xp. Before solving for xp you need to divide the equation by t2 to have the correct forcing function f(t). t2x'' − 2tx' + 2x = 8t xp =__________________

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