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
›
Solve the differential equation dy/dx = 6x^2y.
Solve the differential equation dy/dx = 6x^2y.
Expand All
Collapse All
Practice Questions
1 question
Q1
Solve the differential equation dy/dx = 6x^2y.
y = Ce^(2x^3)
y = Ce^(3x^2)
y = Ce^(6x^2)
y = Ce^(x^6)
Show Solution
Copy
This is a separable equation. Integrating gives y = Ce^(2x^3).
Questions & Step-by-step Solutions
1 item
Q
Q: Solve the differential equation dy/dx = 6x^2y.
Solution:
This is a separable equation. Integrating gives y = Ce^(2x^3).
Steps: 9
Show Steps
Step 1: Identify the differential equation: dy/dx = 6x^2y.
Step 2: Recognize that this is a separable equation, meaning we can separate y and x.
Step 3: Rewrite the equation to separate variables: dy/y = 6x^2 dx.
Step 4: Integrate both sides: ∫(1/y) dy = ∫6x^2 dx.
Step 5: The left side integrates to ln|y|, and the right side integrates to 2x^3 + C (where C is the constant of integration).
Step 6: Write the equation from the integrals: ln|y| = 2x^3 + C.
Step 7: Exponentiate both sides to solve for y: |y| = e^(2x^3 + C).
Step 8: Rewrite e^(C) as a new constant, say C', so |y| = C'e^(2x^3).
Step 9: Since y can be positive or negative, we can drop the absolute value: y = Ce^(2x^3), where C can be any real number.
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..
S
Solve the first-order linear differential equation dy/dx + 2y = 6.
Question: Solve the first-order linear differential equation dy/dx + 2y = 6.Options: y = 3 - Ce^(-2x..
C
Calculate the value of 12 × 8 - 24. (2021)
Question: Calculate the value of 12 × 8 - 24. (2021)Options: 72964860Correct Answer: 72Solution: 12 ..
C
Calculate the area of a triangle with base 10 cm and height 5 cm. (2021)
Question: Calculate the area of a triangle with base 10 cm and height 5 cm. (2021)Options: 25 cm²50 ..
‹
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
✕
↑
