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If y=3\ e^(2x)+2\ e^(3x) , prove that (d...

If `y=3\ e^(2x)+2\ e^(3x)` , prove that `(d^2y)/(dx^2)-5(dy)/(dx)+6y=0` .

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To prove that \(\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0\) for the function \(y = 3e^{2x} + 2e^{3x}\), we will follow these steps: ### Step 1: Find the first derivative \( \frac{dy}{dx} \) Given: \[ y = 3e^{2x} + 2e^{3x} \] ...
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
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  3. If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

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