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Homework-4: Problem 3 Previous Problem Problem List Next Problem (3 points) The general solution of the homogeneous differential equation 4x^2y'' + 9xy' + y = 0 can be written as yc = ax^-1 + bx^(-1/4) where a, b are arbitrary constants and yp = 1 + 2x is a particular solution of the nonhomogeneous equation 4x^2y'' + 9xy' + y = 20x + 1 By superposition, the general solution of the equation 4x^2y'' + 9xy' + y = 20x + 1 is y = yc + yp so y = NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 4, y'(1) = 9 y = The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y1 = x^-1 and y2 = x^-1/4 for the homogeneous equation is W =

          Homework-4: Problem 3

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(3 points)
The general solution of the homogeneous differential equation
4x^2y'' + 9xy' + y = 0
can be written as
yc = ax^-1 + bx^(-1/4)
where a, b are arbitrary constants and
yp = 1 + 2x
is a particular solution of the nonhomogeneous equation
4x^2y'' + 9xy' + y = 20x + 1
By superposition, the general solution of the equation 4x^2y'' + 9xy' + y = 20x + 1 is y = yc + yp so
y =
NOTE: you must use a, b for the arbitrary constants.
Find the solution satisfying the initial conditions y(1) = 4, y'(1) = 9
y =
The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval
The Wronskian W of the fundamental set of solutions y1 = x^-1 and y2 = x^-1/4 for the homogeneous equation is
W =

Homework-4: Problem 3

Previous Problem
Problem List
Next Problem

(3 points)
The general solution of the homogeneous differential equation
4x^2y” + 9xy' + y = 0
can be written as
yc = ax^-1 + bx^(-1/4)
where a, b are arbitrary constants and
yp = 1 + 2x
is a particular solution of the nonhomogeneous equation
4x^2y” + 9xy' + y = 20x + 1
By superposition, the general solution of the equation 4x^2y” + 9xy' + y = 20x + 1 is y = yc + yp so
y =
NOTE: you must use a, b for the arbitrary constants.
Find the solution satisfying the initial conditions y(1) = 4, y'(1) = 9
y =
The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval
The Wronskian W of the fundamental set of solutions y1 = x^-1 and y2 = x^-1/4 for the homogeneous equation is
W =

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