Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
Find the general solution of the equation y'' - 3y' + 2y = 0.
Find the general solution of the equation y'' - 3y' + 2y = 0.
Expand All
Collapse All
Practice Questions
1 question
Q1
Find the general solution of the equation y'' - 3y' + 2y = 0.
y = C1 e^(2x) + C2 e^(x)
y = C1 e^(x) + C2 e^(2x)
y = C1 e^(3x) + C2 e^(0)
y = C1 e^(0) + C2 e^(3x)
Show Solution
Copy
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r-1)(r-2)=0. Thus, the general solution is y = C1 e^(x) + C2 e^(2x).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the general solution of the equation y'' - 3y' + 2y = 0.
Solution:
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r-1)(r-2)=0. Thus, the general solution is y = C1 e^(x) + C2 e^(2x).
Steps: 5
Show Steps
Step 1: Write down the given differential equation: y'' - 3y' + 2y = 0.
Step 2: Identify the characteristic equation by replacing y'' with r^2, y' with r, and y with 1. This gives us r^2 - 3r + 2 = 0.
Step 3: Factor the characteristic equation. Look for two numbers that multiply to 2 and add to -3. The factors are (r - 1)(r - 2) = 0.
Step 4: Set each factor equal to zero to find the roots: r - 1 = 0 gives r = 1, and r - 2 = 0 gives r = 2.
Step 5: Write the general solution using the roots found. The general solution is y = C1 e^(1x) + C2 e^(2x), where C1 and C2 are constants.
Related Questions
F
Find the value of 5! (5 factorial). (2019)
Question: Find the value of 5! (5 factorial). (2019)Options: 12010015090Correct Answer: 120Solution:..
W
What is the value of (3 + 5) × (2 - 1)? (2020)
Question: What is the value of (3 + 5) × (2 - 1)? (2020)Options: 816106Correct Answer: 8Solution: (3..
W
What is the value of 12 ÷ (2 + 4)? (2018)
Question: What is the value of 12 ÷ (2 + 4)? (2018)Options: 2346Correct Answer: 3Solution: 12 ÷ (2 +..
W
What is the square root of 64? (2020)
Question: What is the square root of 64? (2020)Options: 6789Correct Answer: 8Solution: The square ro..
W
What is the solution of the equation y' = -ky, where k is a constant?
Question: What is the solution of the equation y\' = -ky, where k is a constant?Options: y = Ce^(kt)..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
