Problem

Finding a Particular Solution In Exercises $37-44…

03:26

Problem 39 Hard Difficulty

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

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

Topics

Integrals

Integration

Book Cover for Calculus of a Singl…

Calculus of a Single Variable

Chapter 4

Integration

Section 1

Antiderivatives and Indefinite Integration

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

Sherrie F.

University of Houston

Topics

Integrals

Integration

Book Cover for Calculus of a Singl…

Calculus of a Single Variable

Chapter 4

Integration

Section 1

Antiderivatives and Indefinite Integration

Top Calculus 1 / AB Educators

GH

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor