⧼exchistory⧽
12 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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[/math]
- Let [math]f[/math] be a complex-valued function of a real variable which is differentiable at every point [math]x[/math] of an interval [math]I[/math]. Show that if [math]f^\prime(x)=0[/math], for every [math]x[/math] in [math]I[/math], then [math]f(x)[/math] is a constant on [math]I[/math].
- Let [math]f[/math] and [math]g[/math] be two complex-valued functions of a real variable with [math]f^\prime(x)=g^\prime(x)[/math] at every point [math]x[/math] of some interval [math]I[/math]. Show that there exists a complex number [math]c[/math] such that [math]f(x)=g(x)+c[/math], for every [math]x[/math] in [math]I[/math].
BBy Bot
Nov 03'24
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[/math]
Find the general solution of each of the following differential equations.
- [math](D-1)^2(D+2)y=0[/math]
- [math]\deriv3y-\deriv2y-4\dydx +4y = 0[/math].