You can verify that the differential equation: −7x2y′′−14x(x−1)y′+14(x−1)y=0−7x2y″−14x(x−1)y′+14(x−1)y=0, x>0x>0 has solutions y1=3xy1=3x and y2=5xexp(−2x)y2=5xexp⁡(−2x). Compute the...

You can verify that the differential equation: −7x2y′′−14x(x−1)y′+14(x−1)y=0−7x2y″−14x(x−1)y′+14(x−1)y=0, x>0x>0 has solutions y1=3xy1=3x and y2=5xexp(−2x)y2=5xexp⁡(−2x).

Compute the Wronskian WW between y1y1 and y
The solutions y1y1 and y2y2 form a fundamental set of solutions because there is a point x0x0 where W(x0)≠0W(x0)≠0

Expert Solution

Colby Messinger answered 2 years ago

a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential...

a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential equation b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation y'' - y = 0 y1 = e^x, y2 = e^-x : y(0) = 0, y'(0) = 5

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a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation...

a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation x^2 y ″ − 6 x y ′ + 10 y = 0. Let y be the solution of the equation x^2 y ″ − 6 x y ′ + 10 y = 3 x^5 satisfyng the conditions y ( 1 ) = 0 and y ′ ( 1 ) = 1. Find the value of the function f ( x ) = y ( x )...

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(Differential Equations) Consider the differential equation xy’-x4y3+y=0 Verify that the function y = (Cx2-x4)-1/2 is a...

(Differential Equations) Consider the differential equation xy’-x4y3+y=0 Verify that the function y = (Cx2-x4)-1/2 is a solution of the differential equation where C is an arbitrary constant. Find the value of C such that y(-1) = 1. State the solution of the initial value problem. State the interval of existence.

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