Find the particular solution, y= f(x), that satisfies the differential equation f ' (x) = (4x^(3) - 3) * (5x^(2) + 1) and the initial condition of f(3) = 2300.
Please show work.
2007-11-17 07:19:50 · 2 answers · asked by chessmaster2000 2 in Education & Reference ➔ Homework Help
First, take the expression for f'(x) and multiply it out to eliminate the parentheses. Then integrate it. Substitute (3,2300) into the equation and solve for the unknown constant "c".
2007-11-17 07:31:10 · answer #1 · answered by Tim C 7 · 0⤊ 0⤋
Work backwards from your derivative equation. To make it easier, I'd foil first and then find f(x)
f'(x)=20x^5 - 15x^2 + 4x^3 -3
So since the derivative of something is nx^n-1, you can work backwards. For the first term, you'll know its going to be something x^6, so divide 20 by 6. Do that for each term.
f(x)=(10/3)x^6 - 5x^3 - x^4 -3x + ?
It's possible that there is another term at the end which goes away when you take the derivate, which is where the f(3) = 2300 comes in, so plug in 3 and 2300 to find what ? equals
2300=(10/3)3^6 - 5(3)^3 - 3^4 -3(3) + ?
Now solve for ?. I dont have a calculator with me so you can do that.
2007-11-17 07:30:13 · answer #2 · answered by gang$tahtooth 5 · 0⤊ 0⤋