NCERT Class 12 · Ch 9 Exercise 9.3 · Q15
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 15
Find the curve through (0,0) with y′=eˣ sin x.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(\frac{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{2} + \frac{1}{2}\)
- Integrate eˣsin x by parts twice: I=eˣsin x−eˣcos x−I, hence I=eˣ(sin x−cos x)/2.
- Thus y=eˣ(sin x−cos x)/2+C. At (0,0), C=1/2.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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