x2 y" + (x2+x) y’ +(2x-1) y = 0, Find the general solution of y1 with...

x² y" + (x²+x) y’ +(2x-1) y = 0,

Find the general solution of y₁ with r₁ and calculate the coefficient up to c₄ and also find the general expression of the recursion formula, (recursion formula for y₁)
Find the general solution of y₂ based on theorem 4.3.1. (Hint, set d₂ = 0)

Expert Solution

Colby Messinger answered 2 years ago

Find the general solution of y'' + 2(sech^2 t)y = 0 (1), given that y1 =...

Find the general solution of y'' + 2(sech^2 t)y = 0 (1), given that y1 = tanh t is a solution to (1)

Find the general power series solution for the differential equation 2x^2y''-xy'+(x^2 +1) y =0 about x=0...

Find the general power series solution for the differential equation 2x^2y''-xy'+(x^2 +1) y =0 about x=0 (Answer should be given to the x^4+r term)

Consider the following differential equation: x2y"-2xy'+(x2+2)y=0 Given that y1=x cos x is a solution, find a...

Consider the following differential equation: x2y"-2xy'+(x2+2)y=0 Given that y1=x cos x is a solution, find a second linearly independent solution to the differential equation. Write the general solution.

find the general solution (2x+3)dy/dx=(2x+3)/(x^2 +3x+1) -y

Find the solution y'-e^(-2x)=0 , y(0) = 3.5

Find the general solution of the ODE: y'' − 6y' + 9y = (1 + x^2)e^2x...

Find the general solution of the ODE: y'' − 6y' + 9y = (1 + x^2)e^2x .

Obtain the general solution to the following equation. (x2+25)dy/dx + xy = 2x y(0)=4

given y1 find y2 (Differential Equations) (3x-1)y''-(3x+2)y'-(6x-8)y=0 and y1=e^(2x)

Find the general solution for the equations: P(x) y"+ xy' - y = 0 a) P(x)=...

Find the general solution for the equations: P(x) y"+ xy' - y = 0 a) P(x)= x b) P(x)= x2 c) P(x) = 1

1. Find the general solution to the following ODE: y′′′+ 4y′= sec(2x) 2. Find the solution...

1. Find the general solution to the following ODE: y′′′+ 4y′= sec(2x) 2. Find the solution to the following IVP: 2y′′+ 2y′−2y= 6x2−4x−1 y(0) = −32 y′(0) = 5 3. Verify that y1=x1/2ln(x) is a solution to 4x2y′′+y= 0, and use reduction of order to find a second solution y2. 4. Find the general solutions to the following ODEs: a) y′′′−y′= 0. b) y′′+ 2y′+y= 0. c) y′′−4y′+ 13y= 0.

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