Calculus buff (at least 2nd year) needed ASAP!!!! Got an exam in an hr or so and need explanation on a problem!

[Hoeboy]

This particular section is about differentiating equations in the form of y' + P(x)y = Q(x) and multiplying through by I(x)=e^(integral P(x)).

Okay so here is a sample problem:

Solve the differential equation: y' + 3x^2y=6x^2

I(x) = e^X^3

Multiplying through by I(x) gives: (e^x^3) y' + 3x^2(e^x^3)y = 6x^2(e^x^3)

d/dx (e^x^3)y = 6x^2(e^x^3) <<<<<< LOST HERE!!!

Integrating both sides: (e^x^3)y = 2e^x^3 + C

Finally dividing both sides by (e^x^3) gives: y = 2 + C/(e^x^3)

I don't get the step after multiplying both sides by I(x).

 

[thEnEuRoMancER]

It's the reverse of this rule:

d/dx(f(x)*g(x)) =f(x)*g'(x) + f'(x)*g(x)

PM me for details

 

[Hoeboy]

ah. i c. the product rule. i lub choo!

 

[Random Variable]

PRODUCT RULE

d/dx (e^x^3)y = (e^x^3) y' + 3x^2(e^x^3)y

 

[Random Variable]

If Q(x)*l(x) did not have an elementary antiderivative, and you were asked to solve an initial value problem, you could not solve it that way.

 

[MichaelD]

OMG, I feel so stupid and inadequate. I failed high school algebra. Twice. But yet I had no less than a 95 average in English/Composition/Speech/Grammar for all of high school, as well as two years of college. Go figure. I can solve X+3=23, but beyond that, say,

"Johnny is in a train traveling 23Kph, Marcy has 34 oranges that weigh 45 ounces each. If Joe takes the bus from Baghdad traveling 45MPh and Johnny doesn't eat lunch, then how often will Marcy have to stop to pee?" And I will cry.

Calculus? You guys are The Man.