Determine a function y = f(x) such that y' = $\frac { 1 } { 10 }$ y and f(0) = -3?
A) y = -3 $e ^ { ( 1 / 10 ) \times }$
B) y = $\frac { 1 } { 20 }$ $y ^ { 2 }$ - 3
C) y = $e ^ { ( 1 / 10 ) y }$ - 3
D) y = $\frac { 1 } { 10 }$ $e ^ { - 3 x }$
E) none of these

Question

Quizplus · Accepted Answer

The given differential equation is $y' = \frac{1}{10}y$, which is a first-order linear differential equation. The solution to this type of equation is of the form $y = Ce^{kx}$, where $k$ is the constant from the equation. Given $y' = \frac{1}{10}y$, we have $k = \frac{1}{10}$. Using the initial condition $f(0) = -3$, we find $C = -3$. Thus, the solution is $y = -3e^{\frac{1}{10}x}$, which matches choice A.

Determine a Function Y = F(x) Such That Y' = 110\frac { 1 } { 10 }101​

Determine a Function Y = F(x) Such That Y' = $\frac { 1 } { 10 }$