Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 30 days

Continue

Input your name and email to request the answer

Like

Report

Solve the given differential equation.$$\frac{d y}{d x}=k y^{n}, k \text { is a constant. }$$

If $n=1, y=c e^{k x}$ otherwise, $y^{1-n}=k(1-n) x+c$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

01:01

Verify that $y$ is a solut…

03:16

Solve the given differenti…

00:35

Solve the differential equ…

00:50

06:07

10:49

01:13

00:31

No transcript available

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:15

(a) Compute $\frac{d}{d x}\left(\frac{1}{b} \ln (a+b x)\right) ;$ use this t…

01:59

(a) determine a definite integral that will determine the area of the region…

05:48

Evaluate $\int_{R} \int f(x, y) d A$ for $R$ and $f$ as given.(a) $f(x, …

01:03

If $f^{\prime}(x)=2 e^{x},$ sketch the family of solutions.

04:02

The partial differential equation $c^{2} u_{x x}-u_{t t}=0$ where $c$ is a c…

01:02

Solve the given differential equation.$$\frac{d y}{d x}=3 x^{4} y^{4}$$<…

02:11

02:55

Evaluate the given definite integral.$$\int_{0}^{1}(3 x-2)^{4} d x$$

01:52

Determine the area of the indicated region.Region bounded by $f(x)=2 / x…

04:12

Find (a) $f_{x x}(x, y),$ (b) $f_{y y}(x, y),$ (c) $f_{x y}(x, y),$ and $f_{…