Find the general solution of the differential equation and check the result by differentiation. 24t5 dt Step 1 When solving a differential equation, dy = 24t5, it is convenient to write it in the equivalent differential form dy = 24t dt. To find the general solution, we integrate v integrate both sides. Thus. dy = / 24t dt dy v 24t Step 2 Integrate both sides and use the power rule on the right side. 5+1 y = 24 5+1 + C Step 3 dy Thus, the general solution of dt = 24t5 is y = 4t6 + C C +4t6 Step 4 To check for the result, we have to prove that dt = 24t5 = 24

Find the general solution of the differential equation and check the result by differentiation. 24t5 dt Step 1 When solving a differential equation, dy = 24t5, it is convenient to write it in the equivalent differential form dy = 24t dt. To find the general solution, we integrate v integrate both sides. Thus. dy = / 24t dt dy v 24t Step 2 Integrate both sides and use the power rule on the right side. 5+1 y = 24 5+1 + C Step 3 dy Thus, the general solution of dt = 24t5 is y = 4t6 + C C +4t6 Step 4 To check for the result, we have to prove that dt = 24t5 = 24

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Find the general solution of the differential equation and check the result by differentiation.
24t5
dt
Step 1
When solving a differential equation,
dy
- = 24t5, it is convenient to write it in the equivalent differential form dy = 24t$dt. To find
the general solution, we integrate v
integrate both sides.
Thus.
dy = / 24t
dt
dy v
24t
Step 2
Integrate both sides and use the power rule on the right side.
5+1
y = 24
5+1
-C
Step 3
dy
Thus, the general solution of
dt
= 2415 is y = 4t6 + C
C +4t®
Step 4
To check for the result, we have to prove that
dt
= 24t5.
= 24

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