dy/dt= 0.3y-2
y(0)=48
Solve the initial value problem y(t)=?
How can I approach problems which have the differential result of y(t) containing y (instead of x as usual)?
Thank you.

Question

dy/dt= 0.3y-2
y(0)=48
Solve the initial value problem y(t)=?
How can I approach problems which have the differential result of y(t) containing y (instead of x as usual)?
Thank you.

anonymous · Answer

We havent learned integration yet. What else can I do?

anonymous · Answer

antiderivative of function dy/dt=.3y-2 is y^(0.3+1) -2y? It doesn't look right.

tkhunny · Answer

This is a separable differential equation.  It requires to discovery of an antiderivative.  If you have not studied integration, you cannot be expected to solve this problem analytically.  It is possible that graphical methods are intended.

You are given that y = y(t).  You cannot just ignore the t.

$dy/dt= 0.3y-2$

$\dfrac{dy}{0.3y-2} = dt$

$\dfrac{10}{3}\cdot\ln|0.3y - 2| = t + C$

You can continue to solve for y.

If you NEVER have seen anything like this, I have to question you curriculum design.  It just makes no sense to introduce differential equations with no background whatsoever in integration techniques.

anonymous · Answer

Thank you. My prof has only gone over the Newton's Law of Cooling which dy/dt=-ky with y is only a 'helping varies'.

tkhunny · Answer

Fair enough.  If you have gone over Newton's Law of Cooling,  then it is likely that you HAVE seen something like this.  It had, perhaps, a different appearance, but it would have been at least somewhat similar.