The Exponential Solution for the Homogeneous Linear Differential Equation of the
The Exponential Solution for the Homogeneous Linear Differential Equation of the
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11 The notations of Sections 1 and 2 will be used without further comment. As an abbreviation, we define by (^.^) 2 cosh A = y^ + y^ = e.
Now we can state Theorem 2 . If the assumptions 1, 2. , and 5 are satisfied, then (^. 5) Y = (-1)"^ I for X = X, n iS. G) e^ , is a monotonic function of x such that 0' = d0/dx is differ- ent from zero and has the same sign in the whole interval.
Proof : If 0' =0, y^ + y'^ = y| - Qy^ = 0. Therefore, yJ and y^ have the same sign (since Q >0). Therefore, if 0' ...= 0, (^•7) 0^ - i^ = (y^- y^)^ + l^y^y^ - 4 = (y^- y^)^ + hy]^^ > unless '•] — . /p-' Y-i — Yo ~ '-'• (Note that yj^y^ = and y|- Qyg = implies y| = yg = 0).
12 Lemma 2. Let Q > for all x and assume that f^ is differen- tlable everyvhere. If, for a value x >0, x .
What to read after The Exponential Solution for the Homogeneous Linear Differential Equation of the?
You can find similar books in the "Read Also" column, or choose other free books by J Mariani to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
11 The notations of Sections 1 and 2 will be used without further comment. As an abbreviation, we define by (^.^) 2 cosh A = y^ + y^ = e.
Now we can state Theorem 2 . If the assumptions 1, 2. , and 5 are satisfied, then (^. 5) Y = (-1)"^ I for X = X, n iS. G) e^ , is a monotonic function of x such that 0' = d0/dx is differ- ent from zero and has the same sign in the whole interval.
Proof : If 0' =0, y^ + y'^ = y| - Qy^ = 0. Therefore, yJ and y^ have the same sign (since Q >0). Therefore, if 0' ...= 0, (^•7) 0^ - i^ = (y^- y^)^ + l^y^y^ - 4 = (y^- y^)^ + hy]^^ > unless '•] — . /p-' Y-i — Yo ~ '-'• (Note that yj^y^ = and y|- Qyg = implies y| = yg = 0).
12 Lemma 2. Let Q > for all x and assume that f^ is differen- tlable everyvhere. If, for a value x >0, x .
What to read after The Exponential Solution for the Homogeneous Linear Differential Equation of the?
You can find similar books in the "Read Also" column, or choose other free books by J Mariani to read onlineMoreLess
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