solve x^2y^''-4xy^'+6y=lnx^2 y(0)=0, y^'(0)=1

solve

x^2y^''-4xy^'+6y=lnx^2

y(0)=0, y^'(0)=1

Expert Solution

Colby Messinger answered 1 week ago

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a)...

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a) Determine all singular points and find a minimum value for the radius of convergence of a power series solution about x0 = 0. (b) Use a power series expansion y(x) = ∑∞ n=0 anx n about the ordinary point x0 = 0, to find a general solution to the above differential equation, showing all necessary steps including the following: (i) recurrence relation; (ii) determination...

($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

Find the solutions to (-1+x^2)y''+4xy'+2y=0 y_1=? y_2=?

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

Question : y''=4y'+8y=0 , (y''-4y'+13y)^2=0 , (y''+2y'+2y)^2=0 , y''-6y'+13y=0,y(0)=3 , y'(0)=13 , 2y''-6y'+17y=0,y(0)=2, y'(0)=13

Solve the system by Laplace Transform: x'=x-2y y'=5x-y x(0)=-1, y(0)=2

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4

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solve x^2y^''-4xy^'+6y=lnx^2 y(0)=0, y^'(0)=1

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