Other Math Archive: Questions from September 05, 2022
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Which below function is one of the solutions of the differential equation \( y^{\prime}-y=1 \) ? A. \( y=e^{2} \) B. \( y=2 e^{x}+1 \) C. \( y=2 e^{x}-1 \) D. \( y=y^{\prime}-1 \)1 answer -
Solve the differential equation \( y^{\prime \prime}+4 y^{\prime}+4 y=0, y(0)=1 \) and \( y(1)=2 e^{-2} \). A. \( \quad y=e^{-2 t}(1+2 t) \) B. \( y=2 e^{-2 t}+e^{2 t} \) C. \( y=e^{2 t}(1+t) \) D. \(2 answers -
Solve the differential equation \( 2 y^{\prime \prime}+3 y^{\prime}+y=0 \) A. \( y=e^{-\frac{1}{2} t}(A \cos t+B \sin t) \) B. \( y=A e^{-\frac{1}{2} t}+B e^{-t} \) C. \( y=A e^{\frac{1}{2} t}+B e^{t}1 answer -
Solve the differential equation \( \frac{d y}{d x}=3 x^{2} \) and \( y(0)=1 \). A. \( y=x^{3}+c \) B. \( y=x^{3}+1 \) C. \( y=3 x^{3}+c \) D. \( y=6 x+1 \)1 answer -
Solve the differential equation \( 4 y^{\prime \prime}-4 y^{\prime}+y=0 \). A. \( y=e^{\frac{1}{2} t}(A \cos t+B \sin t) \) B. \( y=A e^{\frac{1}{2} t}+B e^{t} \) C. \( y=(A+B t) e^{\frac{1}{2} t} \)1 answer -
Solve the differential equation \( y^{\prime}+y=2 e^{-x} \) and \( y(0)=2 \). A. \( y=2 e^{-x}(x+1) \) B. \( y=e^{-x}(2 x+c) \) C. \( y=e^{x}(2 x+c) \) D. \( y=2 e^{x}(x+1) \)2 answers -
Solve the differential equation \( y^{\prime}=\mathrm{y} \cos x \). A. \( y=c e^{-\sin x} \) B. \( y=c e^{\sin x} \) C. \( y=\frac{y^{2}}{2} \sin x+c \) D. \( y=-\frac{y^{2}}{2} \sin x+c \)1 answer -
Solve the differential equation \( 4 y^{\prime \prime}+y^{\prime}=0 \). A. \( y=e^{-\frac{1}{4} t}(A \cos t+B \sin t) \) B. \( y=A e^{t}+B e^{\frac{1}{4} t} \) C. \( y=(A+B t) e^{-\frac{1}{4} t} \) D.1 answer -
Solve the differential equation \( \frac{d y}{d x}=3 x^{2} \) and \( y(0)=1 \). A. \( y=x^{3}+c \) B. \( y=x^{3}+1 \) C. \( y=3 x^{3}+c \) D. \( y=6 x+1 \)1 answer -
0 answers
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Dado el circuito RC mostrado en la figura: Si \( E(t)=\operatorname{sen}(2 t) \) y la ecuación diferencial del circuito es: \[ i R+\frac{1}{C} \int_{0}^{t} i(\tau) d \tau=E(t) \] Encuentre, a) La cor0 answers -
1 answer