Algebra Archive: Questions from October 07, 2023
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Find a general solution of the following ODEs. (1) \( y^{\prime}-4 x^{3} y=0 \) (2) \( y^{\prime} \tan x=y-4 \) (3) \( \left(x^{2}+y^{2}\right) d y-d x+2 x y d y=0 \) (4) \( x y^{\prime}+y=\sin x \) (1 answer -
Find a general solution of the following ODEs. (4) \( x y^{\prime}+y=\sin x \) (5) \( e^{x}(\sin y d x+\cos y d y)=0 \)1 answer -
A function f is said to be strictly increasing if it holds: - U X X X X (Vx, y ≤ Dƒ) ((x = y) ⇒ (f(x) = f(y))). (x, y ≤ Df) ((x >y) ⇒ (f(x) > f(y)). (Vx, y ≤ Df) ((x >y) ⇒ (f(x)
A function \( f \) is said to be strictly increasing if it holds: \[ \begin{array}{l} \left(\forall x, y \in D_{f}\right)((x=y) \Rightarrow(f(x)=f(y))) . \\ \left(\exists x, y \in D_{f}\right)((x>y) \1 answer -
\( \left\{\begin{array}{rr}x-2 y+3 z= & 4 \\ 2 x+y+z= & -2 \\ -3 x+2 y-2 z= & -1\end{array}\right. \)1 answer