x^2y'' + 9xy' - 20y = 0 Use the substitution x = e^t to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy/dt and ypp for d2y/dt2). Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.
x^2y'' - 7xy' + 16y = 0 Use the substitution x = e^t to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy/dt and ypp for d2y/dt2). Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.
x^2y'' + 6xy' + 4y = x^2 Use the substitution x = e^t to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy/dt and ypp for d2y/dt2). Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.
Solve the given system of differential equations by systematic elimination. (D + 1)x + (D - 1)y = 6 7x + (D + 6)y = -1 (x(t), y(t)) =
Solve the given system of differential equations by systematic elimination. dx/dt = -y + t dy/dt = x - t (x(t), y(t)) =
y'' - y' = 0 Consider the following differential equation to be solved using a power series. Using the substitution y = n = 0 cn x^n, find an expression for ck+2 in terms of ck+1 for k = 0, 1, 2,
y'' + xy = 0 Consider the following differential equation to be solved using a power series. Using the substitution y = n = 0 cn x^n, find an expression for ck+2 in terms of ck-1 for k = 1, 2, 3,
y'' + x^2y = 0 Find two power series solutions of the given differential equation about the ordinary point x = 0.
y'' - 3xy' + y = 0 Find two power series solutions of the given differential equation about the ordinary point x = 0.
(x^2 - 25)y'' + 4xy' + y = 0 Without actually solving the given differential equation, find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 and about the ordinary point x = 1