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Problem 40

Finding a Particular Solution In Exercises $37-44…

03:26
Problem 40

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$f^{\prime}(s)=10 s-12 s^{3}, f(3)=2$
Problem 41

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$f^{\prime \prime}(x)=2, f^{\prime}(2)=5, f(2)=10$
Problem 42

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$f^{\prime \prime}(x)=3 x^{2}, f^{\prime}(-1)=-2, f(2)=3$
Problem 43

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

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$f^{\prime \prime}(x)=\sin x, f^{\prime}(0)=1, f(0)=6$
Sherrie F.
University of Houston
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81
Problem 39

Finding a Particular Solution In Exercises $37-44,$ find the particular solution of the differential equation that satisfies the initial condition(s).
$h^{\prime}(x)=7 x^{6}+5, h(1)=-1$

Answer

$$
h(x)=x^{7}+5 x-7
$$

Chapter 4
Integration
Section 1
Antiderivatives and Indefinite Integration
Calculus of a Single Variable

Topics

Indefinite Integrals

Discussion

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Video Transcript

39. They wanted a toe solve for the initial conditions. So they're given me each crime of X equal seven x to the sick power. Plus I we're a chip one. It was negative. So I'm gonna take my integral, get my original function, plug in my values for my original function and solve for C Take me into Rome. Huge of hex. He won't the integral of seven with six. That's fine. Seven minutes with seven. Your experiment? Yeah, this is really five x to the zero. So when I add on to the rope, get X so us see, I have just next to the seven. X. Now I have to solve for C given eighths of one equals negative one. So when X equals one h, the Becky X equals negative one negative one equals 1227 Sorry. Plus five times one. See negative one. He won't six plus c. Therefore, see who's taking seven. And my answer becomes each of X equals X to the seven. Once my ex minus

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