I need help please!

Question

Find the specific solution of the differential equation  with condition y(-4) = e.

Options:

1)
2)
3)
4)	None of these

Answer 1

Hi Zayn!

This ODE is separable - you can put y's and dy's on one side and x's and dx's on the other. Do this. You'll get:

dy/y = -4dx/x^2

Integrate both sides to get ln(y) + C = -4/x + K, where C and K can be different constants. For simplicity, I'll roll them up into one C on the left hand side, and call this a general solution.

Now, plug in your fact that y(-4) = e. You do this by entering -4 for x and e for y in your general solution. Once you do that, you'll find the value for C, and that gives you your specific solution.

Cheers,

Joe F.

Answer 2

Separate variables.

Then ln y = (-4/x) + C

ln e = 1 = (-4/-4) + C => C=0

y=e^-4/x