Advanced Math Archive: Questions from April 23, 2023
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c) \( \log (2 x+10)=2 \) d) \( \log _{5} x-\log _{5}(x-2)=1 \) e) \( 5^{2 x}=2(5)^{x}+1 \) \( 1-\log (2 x)=0 \)2 answers -
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Problems I. Use the Laplace transform to solve the initial value problems: 1. 2y' + y = 0, y(0) = -3 2. y' - y = 2cos5t, y(0) = 0 3. y" + 5y' + 4y = 0, y'(0) = 0, y(0) = 1 4. y" - 4y' = 6e³t - 3e-t,
I. Use the Laplace transform to solve the initial value problems: 1. \( 2 y^{\prime}+y=0, \quad y(0)=-3 \) 2. \( y^{\prime}-y=2 \cos 5 t, y(0)=0 \) 3. \( y^{\prime \prime}+5 y^{\prime}+4 y=0, y^{\prim2 answers -
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Identifique si la función es implicita o explicita. Una vez lo identifique, conviértela al otro modo. 1. \( 2 x+3 y+5 \) 2. \( 2 x+6=y \) Combine funciones \[ F(x)=3 x+1 ; g(x)=4 x+3 \] 1. \( (f+g)(0 answers -
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Classify the equilibrium points of nonlinear systems. \[ \begin{array}{l} x^{\prime}=y+y^{2} \\ y^{\prime}=x+y \end{array} \] \[ \begin{array}{l} x^{\prime}=x(3-y) \\ y^{\prime}=x+y+1 \end{array} \] \2 answers -
Find a formula for the solution of the initial value problem. (a) \( y^{\prime \prime}+3 y^{\prime}+y=f(t), \quad y(0)=0, \quad y^{\prime}(0)=0 \) (b) \( y^{\prime \prime}+4 y=f(t), \quad y(0)=0, \qua2 answers -
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