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Problem 43 Hard Difficulty

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$f^{\prime \prime}(x)=x^{-3 / 2}, f^{\prime}(4)=2, f(0)=0$


$-4 \sqrt{x}+3 x$


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Video Transcript

for real aren't getting double crime. Thanks equals negative X to the neighboring. Three have and Rome four equals team and of zero hero. They justify the admission condition. For the first thing you do is take the logo of a double crime. And then from eggs He was the anti roll, huh, ext? Negative. Three halves. Yeah, Add one. My, I have X, a negative one. Bye bye, Bill. Maybe the U So negative too. It's the 1/2 the 1/2 makes it a square root. The negative puts it in the denominator. So every time we'll see. Now we know that when prime when exits for that crime is to something. Two. I have negative too. Oh, this here water. Let's see. And that gives me two over. Negative one to be one negative one plus c four c b three. So they are going to take The integral eggs will now eat will be in control. Um oh, negative to x with maybe 1/2 hour. Yes. Give me negative too. Add one. That's gonna be a positive 1/2 and multiplied by the reciprocal and plus three. I really have plus three x to the zeros. So I'm gonna have see And then we have to find out what See? So we know that every Becks zero when x zero, Why is the room so I have negative were X to the 1/2 plus three x Last thing equals my f of X. So when X equals zero, everything's going to kids a lot and see with them after equals zero. So my function my ex, it's just people negative core that's a plus.