Suppose $y ^ { \prime } = y$ and $y ( 1 ) = 4$ .What is the best approximation of $y ( 1.2 )$ .
A)0.8
B)3.6
C)4.8
D)16

Question

Quizplus · Accepted Answer

Given $y' = y$ and $y(1) = 4$, this is a differential equation whose solution is $y = Ce^{kt}$, where $C$ and $k$ are constants. Since $y(1) = 4$, we can find that $C \cdot e^k = 4$. The general solution for $y' = y$ is $y = Ce^t$, implying $k = 1$. Thus, $y(t) = Ce^t$. With $y(1) = 4$, we find $C = 4/e$. To approximate $y(1.2)$, we use $y(t) = 4e^{t-1}$. Plugging in $t = 1.2$, $y(1.2) = 4e^{0.2}$. Since $e^{0.2}$ is approximately $1.2$, $y(1.2) \approx 4 \times 1.2 = 4.8$.

Suppose y′=yy ^ { \prime } = yy′=y And y(1)=4y ( 1 ) = 4y(1)=4

Suppose $y ^ { \prime } = y$ And $y ( 1 ) = 4$