Mathbee CBSE Mathbee · CBSE Class 12 Maths
NCERT Class 12 · Ch 5 Exercise 5.7 · Q13

NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 13

If y=\(4 \sin{\left(\log{\left(x \right)} \right)} + 3 \cos{\left(\log{\left(x \right)} \right)}\), show x²y″+xy′+y=0.

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: x²y″+xy′+y=0
  1. First derivative: y′=\(- \frac{3 \sin{\left(\log{\left(x \right)} \right)}}{x} + \frac{4 \cos{\left(\log{\left(x \right)} \right)}}{x}\).
  2. Second derivative: y″=\(- \frac{\sin{\left(\log{\left(x \right)} \right)} + 7 \cos{\left(\log{\left(x \right)} \right)}}{x^{2}}\).
  3. Substitution into the indicated left-hand combination and simplification gives \(0\). Work with x>0 for log x.

Master Chapter 5: Continuity And Differentiability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
For y=cos⁻¹x, express y″ in terms of y alone.
Next Question →
If y=\(A e^{m x} + B e^{n x}\), show y″−(m+n)y′+mny=0.

All Questions in Continuity And Differentiability — Exercise 5.7

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17

Related Questions in Continuity And Differentiability

Class 12 Continuity And Differentiability · Mcq Single Correct
For k<0, define f(x)=(1−cos(kx))/(x sin x) for nonzero x near 0, and f(0)=1/2. Find k for…
Class 12 Continuity And Differentiability · Mcq Single Correct
Near π/2, f(x)=k cos x/(π−2x) for x≠π/2 and f(π/2)=3. Find k for continuity.
Class 12 Continuity And Differentiability · Mcq Single Correct
Find the full set of real inputs excluded from the natural domain of cot x (its poles).
Class 12 Continuity And Differentiability · Mcq Single Correct
How many real inputs are excluded from the original formula f(x)=(x−1)/[x(x²−1)]?
Class 12 Continuity And Differentiability · Mcq Single Correct
For x≠0, f(x)=(e^(3x)−e^(−5x))/x, and f(0)=k. Find k for continuity at 0.
Class 12 Continuity And Differentiability · Mcq Single Correct
Let f(x)=x/|x| for x<0 and f(x)=−1 for x≥0. What is its complete continuity set?