Use la transformada de La Place para resolver la ecuación Diferencial y obtener \( Y(\mathrm{~S}) \) \( 2 y^{\prime \prime \prime}+3 y^{\prime \prime}-3 y^{\prime}-2 y=e^{-t} \) \( y(0)=0 \quad y^{\prime}(0)=0 \quad y^{\prime \prime}(0)=1 \)

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and \( b \) is the brain mass grams). Suppose the brain mass of a \( 20-\mathrm{g} \) fetus is changing at a rate of 0.23 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \).

El volumen se calcula mediante una integral doble sobre la base del plano (zy) y la alurara \( z(z, y) \). Ya sabemos que lo equación del plano es: \[ z=11-\frac{11 e}{0}-\frac{11 y}{10} . \]

\( \int _ { - 1 } f ( x ^ { 2 } - 1 ) d x = \lim _ { n \rightarrow \infty } [ \sum _ { i = 1 } ^ { n } \frac { 3 - ( - 1 ) } { n } \cdot f ( ( - 1 ) + i \cdot \frac { 3 - ( - 1 ) } { n } ) ] \)

\( d y ( d x - ( 1 - x ) y ^ { 2 } = ( 2 x - 1 ) y - x \)

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain ma: grams). Suppose the brain mass of a \( 21-\mathrm{g} \) fetus is changing at a rate of 0.26 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \). \( \frac{\mathrm{dm}}{\mathrm{dt}}=\square \mathrm{g} \) per day (Round to five decimal places as needed.)