Applied Mathematics

Calculus

Medium

applied

If $y = 3e^{2x} + 2e^{3x}$ , then which one of the following is true ?

$\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0$

$\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0$

$\frac{d^2y}{dx^2} - 5\frac{dy}{dx} - 6y = 0$

$\frac{d^2y}{dx^2} + 5\frac{dy}{dx} - 6y = 0$

✅ Correct Option: 2

$y'=6e^{2x}+6e^{3x}$ , $y''=12e^{2x}+18e^{3x}$ .

Check $y''-5y'+6y$ :

$=12e^{2x}+18e^{3x}-30e^{2x}-30e^{3x}+18e^{2x}+12e^{3x}=0$ .

So $\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y=0$ .

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If y=3e2x+2e3xy = 3e^{2x} + 2e^{3x}y=3e2x+2e3x, then which one of the following is true ?

Solution

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If $y = 3e^{2x} + 2e^{3x}$ , then which one of the following is true ?