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# Solution for If Y = 3 E2x + 2 E3x, Prove that D 2 Y D X 2 − 5 D Y D X + 6 Y = 0 ? - CBSE (Commerce) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

If y = 3 e2x + 2 e3x, prove that  $\frac{d^2 y}{d x^2} - 5\frac{dy}{dx} + 6y = 0$ ?

#### Solution

Here,

$y = 3 e^{2x} + 2 e^{3x}$

$\text {Differentiating w . r . t . x, we get }$

$\frac{d y}{d x} = 6 e^{2x} + 6 e^{3x}$

$\text { Differentiating again w . r . t . x, we get }$

$\frac{d^2 y}{d x^2} = 12 e^{2x} + 18 e^{3x}$

$\Rightarrow \frac{d^2 y}{d x^2} = 5\left( 6 e^{2x} + 6 e^{3x} \right) - 6\left( 3 e^{2x} + 2 e^{3x} \right)$

$\Rightarrow \frac{d^2 y}{d x^2} = 5\left( \frac{dy}{dx} \right) - 6y$

$\Rightarrow \frac{d^2 y}{d x^2} - 5\left( \frac{dy}{dx} \right) + 6y = 0$

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Solution If Y = 3 E2x + 2 E3x, Prove that D 2 Y D X 2 − 5 D Y D X + 6 Y = 0 ? Concept: Simple Problems on Applications of Derivatives.
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