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Question #40359

Difficulty: 8/10 | 🟢 Free

The Question

Let $y = y(x)$ be a continuous solution to the differential equation $\frac{dy}{dx} + 3x|x| y = 3x^2$ for all $x \in \mathbb{R}$ . If $y(1) = 1 + \frac{1}{e}$ , then the value of $y(-1)$ is

Options

A.
$\frac{3}{e} - 1$
B.
$1 + e$
C.
$\frac{1}{e} - 1$
D.
$1 + \frac{1}{e}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Monster

Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.

Concepts Behind This Question

Modulus Function Symmetry|Linear Differential Equation Structure|Integration Constant Trap

Why This Question Is Tricky

Common Mistakes

This question tests the 'Integration Constant Trap' within a piecewise linear differential equation defined by modulus symmetry.

Students often ignore the modulus, leading to a single incorrect integration constant across the entire domain (yielding $1+e$ ).

Alternatively, they may correctly split the domain but incorrectly assume the integration constant is identical for both sub-domains ( $C_1=C_2$ ), yielding $\frac{1}{e}-1$ .

The core discriminator is recognizing that continuity at the boundary ( $x=0$ ) is the necessary condition to patch the distinct integration constants together.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Relations and Functions - Class 11
Concept	Modulus Function Symmetry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free