Better Students Ask More Questions.
Find the particular solution of the differential equation x^3 dy/dx = 2 given y = 3 ,...
1 Answer | add yours
We must solve the differential equation:
`x^3 dy/dx = 2`
The first step is to notice that this is a separable equation, so we will separate:
`dy = 2/x^3 dx`
Next, we can integrate both sides:
`int dy = int 2/x^3 dx`
`\implies y = -1/x^2 + c`
We have now found the general solution, and can proceed to solve the initial value problem. We'll plug in y=3 and x=1:
`3 = -1/1 + c \implies c=4`
Therefore our final solution is `y = -1/x^2 + 4`
Posted by mfonda on April 26, 2012 at 7:20 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.