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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY4 Marks
Question
If y = 3e2x + 2e3x, prove that

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

✓

Answer

$\frac{\text{dy}}{\text{dx}}=6\text{ e}^{\text{2x}}+6\cdot\text{e}^{\text{3x}}$

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

$\Rightarrow\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-5\frac{\text{dy}}{\text{dx}}+6\text{y}$ = (12 e2x + 18 e 3x) -5 (6 e2x + 6 e3x ) + 6 (3 e2x + 2 e3x)

= 30 e2x - 30 e2x + 30 e3x - 30 e3x = 0.

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