If y=3e2x+2e3x. Prove that dx2d2y−5dxdy+6y=0.

Solution: y=3e2x+2e3x⇒dxdy=3e2x(2)+2e3x(3)⇒dxdy=6(e2x+e3x)⇒dx2d2y=6(2e2x+3e3x)Now,L.H.S.=dx2d2y−5dxdy+6y=12e2x+18e3x−30e2x−30e3x+18e2x+12e3x=0=R.H.S.

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If {y}={3}{e}^{{{2}{x}}}+{2}{e}^{{{3}{x}}}. Prove that {{{d}^{

Question

If $y = 3 e^{2 x} + 2 e^{3 x}$ . Prove that $\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 0$ .

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

. Prove that

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 0

9 mins ago

Discuss this question LIVE

9 mins ago

Solution:

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

\Rightarrow \frac{d y}{d x} = 3 e^{2 x} (2) + 2 e^{3 x} (3)

\Rightarrow \frac{d y}{d x} = 6 (e^{2 x} + e^{3 x})

\Rightarrow \frac{d ^{2} y}{d x ^{2}} = 6 (2 e^{2 x} + 3 e^{3 x})

Now,

L . H . S . = \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y

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

= 0 = R . H . S .

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Question Text	If $y = 3 e^{2 x} + 2 e^{3 x}$ . Prove that $\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 0$ .
Answer Type	Text solution:1
Upvotes	151