Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Differential Equations · Short Answer2 Markslinear_differential_equations

Class 12 Maths · Differential Equations · Short Answer #92

Solve y′ = y/x.

✅ Step-by-Step Solution

Final Answer: y = Cx, x ≠ 0.
  1. Write the linear equation y′ − y/x = 0; IF = 1/x on a nonzero connected interval.
  2. Then (y/x)′ = 0, so y/x = C. This method does not divide by y and retains C = 0.
  3. Thus y = Cx for x ≠ 0.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Write the linear equation y′ − y/x = 0; IF = 1/x on a nonzero connected interval.
  • [1 mark] Then (y/x)′ = 0, so y/x = C. This method does not divide by y and retains C = 0.
  • [0.5 marks] Thus y = Cx for x ≠ 0.

Master Chapter 9: Differential Equations

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Solve y′ − y(x + 1)/x = 0.
Next Question →
Find an integrating factor of y′ + y = (1 + y)/x.

More Practice Questions in Differential Equations

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Differential Equations

Class 12 Differential Equations · Mcq Single Correct
Find the degree of x²y″ = (xy′ − y)³.
Class 12 Differential Equations · Mcq Single Correct
Find the degree of y″ + 3(y′)² = x² ln(y″).
Class 12 Differential Equations · Mcq Single Correct
Find the order and degree of [1 + (y′)²]² = y″.
Class 12 Differential Equations · Mcq Single Correct
The nonconstant solutions of 2xy′ − y = 3 lie on a family of which curves?
Class 12 Differential Equations · Mcq Single Correct
Find an integrating factor of (x ln x)y′ + y = 2 ln x, for x > 0, x ≠ 1.
Class 12 Differential Equations · Mcq Single Correct
Which function satisfies (y′)² − xy′ + y = 0?