## y2o2 3 years ago Solve it ... if you can :) f(x) + f´(x) = x³ + 5x² + 2

1. dumbcow

\[\large f(x) = x^{3}+2x^{2}-4x+6+Ce^{-x}\]

2. y2o2

Nope, that's not the answer , and don't try integration.

3. dumbcow

really, oh ok i just solved it like it was a linear ODE

4. dumbcow

actually it is right http://www.wolframalpha.com/input/?i=y%27+%2By+%3D+x^3+%2B5x^2%2B2

5. y2o2

No , it's not . the function doesn't contain any unknown but "x".

6. dumbcow

? C is just a constant, you have to provide an initial value or a point to get a particular solution

7. y2o2

f(x) + f´(x) = x³ + 5x² + 2 so x³ + 5x² + 2 is the function plus its derivative so you you have to extract from x³ + 5x² + 2 a function and it's derivative x³ is the highest power , so it must belong to f(x) so f(x) = x³ +... and f´(x) = 3x²+... so f(x) = x³ + 2x²+... , so that 2x² + 3x² = 5x²+... and f´(x) = 3x² + 4x+... so f(x) = x³ + 2x² - 4x+... , so that -4x+4x =0 f´(x) = 3x² + 4x-4 f(x) = x³ + 2x² - 4x + 6 so that -4+6 = 2 f(x) + f´(x) = (x³+2x²-4x+6 )+ (3x²+4x-4) = x³+5x²+2

8. dumbcow

oh i see you solved it intuitively, well we are both correct if i make C=0 your answer is only 1 of many possible solutions to the differential equation

9. dumbcow

great work though :)

10. y2o2

thank you :)