The differential equation representing the curve y = e^2x(a + bx), where a, b are arbitrary constants is Option 1: d^2y/dx^2 + 4dy/dx + 4y = 0 Option 2: d^2y/dx^2 - 4dy/dx - 4y = 0 Option 3: d^2y/dx^2 - 4dy/dx + 4y = 0 Option 4: d^2y/dx^2 + 4dy/dx - 4y = 0

The answer is 'd^2y/dx^2 - 4dy/dx + 4y = 0'. View full solution:

Calculus > Differential Equations

Medium

applied

The differential equation representing the curve $y = e^{2x}(a + bx)$, where a, b are arbitrary constants is

$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$

$\frac{d^2y}{dx^2} - 4\frac{dy}{dx} - 4y = 0$

$\frac{d^2y}{dx^2} - 4\frac{dy}{dx} + 4y = 0$

$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} - 4y = 0$

✅ Correct Option: 3

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