The particular solution of the differential equation dy/dt=2*y for which y(0) = 60 is
y = 60e2t
y = 60 e0.5t
y = 59 + et
y = 30et
The particular solution of the differential equation dy/dt=2*y for which y(0) = 60 is
y = 60e2t
y = 60 e0.5t
y = 59 + et <- my ansswer
y = 30et
To find the particular solution of the given differential equation dy/dt = 2y with the initial condition y(0) = 60, we need to solve the differential equation and substitute the initial condition.
Step 1: Solve the differential equation dy/dt = 2y
We can separate the variables to solve the differential equation. Rearrange the equation:
dy/y = 2dt
Integrate both sides with respect to their respective variables:
∫dy/y = ∫2dt
ln|y| = 2t + C
Where C is a constant of integration.
Step 2: Apply the initial condition y(0) = 60
Substitute t = 0 and y = 60 into the equation ln|y| = 2t + C:
ln|60| = 2(0) + C
ln|60| = C
Step 3: Write the solution and solve for y
Substitute the value of C into the equation ln|y| = 2t + C:
ln|y| = 2t + ln|60|
Since ln|y| and ln|60| are both natural logarithms of positive numbers, we can remove the absolute value signs.
ln(y) = 2t + ln(60)
Exponentiate both sides to eliminate the logarithm:
e^(ln(y)) = e^(2t + ln(60))
y = e^(2t) * e^(ln(60))
y = e^(2t) * 60
Simplify the expression by recognizing that e^(ln(60)) is simply 60:
y = 60 * e^(2t)
So, the particular solution of the differential equation dy/dt = 2y with the initial condition y(0) = 60 is:
y = 60 * e^(2t)