using series to solve differential equations using series to solve differential equations 1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1

using series to solve differential equations

1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1

Expert Solution

Colby Messinger answered 2 years ago

solve xy''-xy'+y=0 (using center series solution)

solve using series solutions (x^+1)y''+xy'-y=0

Find two power series solutions of the following differential equations. y'' - xy' = 0

5. y′′ + xy′ = 0, x0 = 0 Series Solution Method. solve the given differential...

5. y′′ + xy′ = 0, x0 = 0 Series Solution Method. solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution.

y''+xy'+(2x^2+1)y=0 Use power series to find at least four terms of the following differential equations

Differential Equations Use a series solution to solve the IVP . y′′−4y= 0 y(0) = 3...

Differential Equations Use a series solution to solve the IVP . y′′−4y= 0 y(0) = 3 y′(0) = 5. (Your answer will use one or more series.)

Solve the following differential equation using the power series method. (1+x^2)y''-y'+y=0

(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.

Differential Equations: Find the general solution by using infinite series centered at a. 4.xy′′+ y′− y...

Differential Equations: Find the general solution by using infinite series centered at a. 4.xy′′+ y′− y = 0, a=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...

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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