Differential Equations
NCERT Class 12
CBSE
Grade 12
Question:
Find the particular solution of $(1 + e^{2x}) dy + (1 + y^2) e^x dx = 0$ given $y = 1$ when $x = 0$.
Step-by-Step Solution
$\tan^{-1} y = -\tan^{-1}(e^x) + C$. At $x=0, y=1 \Rightarrow C = \pi/2$. [1.5 Marks]
$\tan^{-1} y + \tan^{-1}(e^x) = \dfrac{\pi}{2}$. [1.5 Marks]
---
🎯 Official CBSE Marking Scheme:
Finding constant $C = \pi/2$: 1.5 Marks
Evaluating particular solution: 1.5 Marks
Correct Answer:
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.