Can You Solve This Easy Differential Equation ?

Level 1

Next We Have the Equation

y = 6 x 2 + x 5 y' = 6x^2 +x -5

Taking as initial condition y ( 0 ) = 2 y(0)= 2

Find y ( 4 ) y(4)


The answer is 118.

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2 solutions

Cody Johnson
Mar 29, 2014

By the fundamental theorem of calculus,

f ( 4 ) = f ( 0 ) + 0 4 f ( x ) d x = 2 + 0 4 ( 6 x 3 + x 5 ) d x = 118 f(4)=f(0)+\int_0^4f'(x)dx=2+\int_0^4(6x^3+x-5)dx=\boxed{118}

Nice. But I like my solution. :D

Finn Hulse - 7 years, 2 months ago
Finn Hulse
Mar 29, 2014

First let us take the antiderivative of both sides. This evaluates to y = 2 x 3 + x 2 2 5 x + C y=2x^{3}+\frac{x^{2}}{2}-5x+C . We can plug in zero to this equation and set it equal to two to solve for C C . Thus, 0 + C = 2 0+C=2 and C C equals two. From there, with our general form, we can plug in four and get 118 \boxed{118} .

Very Easy , I'm Starting With Differential Equations !

In Soon I Hope Make Hard Questions !

Vote Up For You !!

Gabriel Merces - 7 years, 2 months ago

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At least give this problem rating. I hate when answering a problem but get nothing. :D

Tunk-Fey Ariawan - 7 years, 2 months ago

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My problems Are All Easy!

Gabriel Merces - 7 years, 2 months ago

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@Gabriel Merces Uh... do you need to capitalize all of your words?

Finn Hulse - 7 years, 2 months ago

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@Finn Hulse @Finn Hulse Gabriel is a bit newbie at english,, So he has such minor errors....

Dinesh Chavan - 7 years, 2 months ago

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@Dinesh Chavan Exactly Dinesh , Thanks !

Gabriel Merces - 7 years, 2 months ago

@Gabriel Merces Please don't use punctuation mark in the end of your comment. It sounds you are angry. :)

Tunk-Fey Ariawan - 7 years, 2 months ago

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