Solve y'=1-xy, y(0)=1

Expert Solution

Colby Messinger answered 1 year ago

Solve by reduction of order xy" - xy' + y = 0

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

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

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

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

Use power series to solve the initial value problem x^2y''+xy'+x^2y=0, y(0)=1, y'(0)=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.

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Solve y'=1-xy, y(0)=1

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