Find the solution of the given initial value problem in explicit form.
y' = (1 - 11x)y^2, y(0) = -1/5
Enclose numerators and denominators in parentheses. For example, (a - b) / (1 + n).
y(x) = 1/(-x + 11/2x^2) + 21/50
Find the solution of the given initial value problem in explicit form.
sin(2x) dx + cos(7y) dy = 0, y(pi/2) = pi/7
Enclose arguments of functions in parentheses. For example, sin(2x).
y = (cos(2x))/2 = (sin(7y))/7
Find the general solution of the given differential equation, and use it to determine how solutions behave as t -> infinity.
y' + 5y = t + e^(-3t)
y = t/5 - 1/25 + 1/(2e^(3t)) + c/e
Solutions converge to the function y =