All Categories
Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
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 first-order linear differential equation dy/dx + y/x = x.
Solve the first-order linear differential equation dy/dx + y/x = x.
Expand All
Collapse All
Practice Questions
1 question
Q1
Solve the first-order linear differential equation dy/dx + y/x = x.
y = x^2 + C/x
y = Cx^2 + x
y = C/x + x^2
y = x^2 + C
Show Solution
Copy
Using the integrating factor e^(∫(1/x)dx) = x, we can solve the equation.
Questions & Step-by-step Solutions
1 item
Q
Q: Solve the first-order linear differential equation dy/dx + y/x = x.
Solution:
Using the integrating factor e^(∫(1/x)dx) = x, we can solve the equation.
Steps: 10
Show Steps
Step 1: Identify the differential equation: dy/dx + y/x = x.
Step 2: Recognize that this is a first-order linear differential equation.
Step 3: Find the integrating factor. The integrating factor is e^(∫(1/x)dx).
Step 4: Calculate the integral: ∫(1/x)dx = ln|x|.
Step 5: Therefore, the integrating factor is e^(ln|x|) = |x|. Since x is positive in this context, we use x.
Step 6: Multiply the entire differential equation by the integrating factor x: x(dy/dx) + y = x^2.
Step 7: Notice that the left side is the derivative of (y * x): d/dx(y * x) = x^2.
Step 8: Integrate both sides: ∫d/dx(y * x) dx = ∫x^2 dx.
Step 9: This gives us y * x = (1/3)x^3 + C, where C is the constant of integration.
Step 10: Solve for y: y = (1/3)x^2 + C/x.
Related Questions
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 -..
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 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 integral ∫(2x)dx from 0 to 2?
Question: What is the value of the integral ∫(2x)dx from 0 to 2?Options: 4231Correct Answer: 4Soluti..
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
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
✕
↑
