All Categories
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 particular solution of dy/dx = 2x with the initial condition y(0) = 1.
Find the particular solution of dy/dx = 2x with the initial condition y(0) = 1.
Expand All
Collapse All
Practice Questions
1 question
Q1
Find the particular solution of dy/dx = 2x with the initial condition y(0) = 1.
y = x^2 + 1
y = x^2 - 1
y = 2x + 1
y = 2x - 1
Show Solution
Copy
Integrating gives y = x^2 + C. Using the initial condition y(0) = 1, we find C = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the particular solution of dy/dx = 2x with the initial condition y(0) = 1.
Solution:
Integrating gives y = x^2 + C. Using the initial condition y(0) = 1, we find C = 1.
Steps: 8
Show Steps
Step 1: Start with the differential equation dy/dx = 2x.
Step 2: Integrate both sides with respect to x. This means we find the integral of 2x.
Step 3: The integral of 2x is x^2 + C, where C is a constant.
Step 4: Now we have the general solution: y = x^2 + C.
Step 5: Use the initial condition y(0) = 1 to find the value of C.
Step 6: Substitute x = 0 into the equation: y(0) = 0^2 + C = C.
Step 7: Set C equal to 1 because y(0) = 1.
Step 8: Now we have the particular solution: y = x^2 + 1.
Related Questions
F
Find the value of tan(45°).
Question: Find the value of tan(45°).Options: 01undefined√3Correct Answer: 1Solution: tan(45°) = 1...
W
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
Question: What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?Options: 3x^2 - 6x + 43x^2 - 6x2x^2 -..
W
What is the value of 5C2?
Question: What is the value of 5C2?Options: 1020155Correct Answer: 10Solution: 5C2 = 5! / (2!(5-2)!)..
W
What is the value of the limit lim (x -> 0) (sin(5x)/x)?
Question: What is the value of the limit lim (x -> 0) (sin(5x)/x)?Options: 01510Correct Answer: 5Sol..
I
If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is
Question: If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the dista..
‹
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
✕
↑
