Advanced Math Archive: Questions from August 06, 2022
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Solve the following \( \mathrm{DE} \) (a) \( \frac{d y}{d x}+y=6 x^{2} y \) (b) \( \frac{d y}{d x}=x e^{-y}+10 e^{-y} \)1 answer -
\( 22(20 \mathrm{pt}) \). Solve the following initial value problems. (a) \( y^{\prime \prime}+9 y=\sin 2 x ; y(0)=1, y^{\prime}(0)=0 \). (b) \( y^{\prime \prime}-2 y^{\prime}+y=1+e^{x} ; y(0)=0, y^{\1 answer -
3 answers
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If \( y \) is a salution of I ip \[ y^{\prime \prime \prime}-y^{\prime \prime}+9 y^{\prime}-9 y=0, \quad y(0)=1, y^{\prime}(0)=9, y^{\prime \prime}(0)=-9 \text {. } \] Find \( y\left(\frac{\pi}{2}\rig1 answer -
\( 2(20 \mathrm{pt}) \). Solve the following initial value problems. (a) \( y^{\prime \prime}+9 y=\sin 2 x ; y(0)=1, y^{\prime}(0)=0 \). (b) \( y "-2 y^{\prime}+y=1+e^{x} ; y(0)=0, y^{\prime}(0)=1 \).1 answer -
1 answer