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Problem 42

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).

$f^{\prime \prime}(x)=3 x^{2}, f^{\prime}(-1)=-2, f(2)=3$

Answer

$$

f(x)=\frac{x^{4}}{4}-x+1

$$

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## Discussion

## Video Transcript

So we're okay to find Vex when medical primal burgs is three x squared crime. Negative one. It's native to good of two three. First thing we do no negative, too. I'm sorry. Yeah, I think it kind of works. That's the antiterror. Don't cry, Jax, which is the attentive relative of three X squared Piak that we make the two here. Three. Divide by three. Yeah, execute because man plies make it two. Which is that's crime making one. She's negative one of you to play one. See, which tells us that, Sig it's a negative one, Really. Should we go to the factory of the crime techs and Lex, which is equal to come on inside the X cubed minus one Thanks, which is X to the fourth divide that by four my specs close some other constant do well, another negative, too. All right. Three two of two two people 2 1/4 to the fourth, minus two because Dean to the forthis 16 that's 16 developed before, which is for minus two close. So let's two costumes, and that all goes together to tell us the D is equal to negative one. That means that this 1/4 thanks forthe finals my swan. That makes sense

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