Other Math Archive: Questions from January 26, 2023
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\( y=C_{1} e^{5 x}+C_{2} e^{-3 x} \) is the general solution of \( y^{\prime \prime}-2 y^{\prime}-15 y=0 \). Find the solution which satisfies the initial conditions \( y(0)=7, y^{\prime}(0)=3 \). (a)2 answers -
Find \( x \) and \( y \). \[ \left[\begin{array}{rrr} x+2 & 8 & -9 \\ 3 & 2 y & 2 x \\ 5 & -8 & y+2 \end{array}\right]=\left[\begin{array}{rrr} 2 x+6 & 8 & -9 \\ 3 & 10 & -8 \\ 5 & -8 & 7 \end{array}\2 answers -
Solve the initial value problem.(h-i)
(e) \( y^{\prime \prime}=x e^{2 x}, \quad y(0)=7, \quad y^{\prime}(0)=1 \) (f) \( y^{\prime \prime}=-x \sin x, \quad y(0)=1, \quad y^{\prime}(0)=-3 \) (g) \( y^{\prime \prime \prime}=x^{2} e^{x}, \qua2 answers