$\text { Find the function } y = f ( t ) \text { passing through the point } ( 0,12 ) \text { with the first derivative }$ $\frac { d y } { d t } = \frac { 6 } { 7 } y$
A)$y ( t ) = e ^ { \frac { 6 } { 7 } t ^ { 2 } } + 12$
B) $y ( t ) = \frac { 6 } { 7 } t ^ { 2 } + 12$
C) $y ( t ) = 12 e ^ { \frac { 6 } { 7 } t ^ { 2 } }$
D)$y ( t ) = 12 e ^ { \frac { 6 } { 7 } t }$
E)$y(t)=e^{\frac{6}{7} t}+12$

Question

Quizplus · Accepted Answer

Given the differential equation $\frac{dy}{dt} = \frac{6}{7}y$ and the initial condition $y(0) = 12$, the solution is of the form $y(t) = Ce^{\frac{6}{7}t}$. Substituting the initial condition yields $C = 12$, so the correct function is $y(t) = 12e^{\frac{6}{7}t}$.

Find the function y=f(t) passing through the point (0,12) with the first derivative \text { Find the function } y = f ( t ) \text { passing through the point } ( 0,12 ) \text { with the first derivative } Find the function y=f(t) passing through the point (0,12) with the first derivative

$\text { Find the function } y = f ( t ) \text { passing through the point } ( 0,12 ) \text { with the first derivative }$