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Which of the following is a solution of \frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=0?

  • Option 1)

    y=ae^{x}-be^{2x}

  • Option 2)

    y=ae^{x}+be^{2x}

  • Option 3)

    y=ae^{x}+b

  • Option 4)

    y=mx+c

 

Answers (1)

best_answer

As we learnt

 

Solution of differential equations -

 

A function y =f(x) is a solution of differential equation, if the substitution of f(x) and its derivative (s) in differential equation reduces it to an identity.

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 On evaluating,\frac{dy}{dx}\; and\; \frac{d^{2}y}{dx^{2}}  from each option and putting in differential equation,,option(A) will satisfy.

y=ae^{x}-be^{2x}

\frac{dy}{dx}=ae^{x}-2be^{2x}

\frac{d^{2}y}{dx^{2}}=ae^{x}-4be^{2x}

Now,\frac{d^{2}y}{dx^{2}}-3\left ( \frac{dy}{dx} \right )+2y=\left ( ae^{x}-4be^{2x} \right )-3\left ( ae^{x}-2be^{2x} \right )+2\left ( ae^{x}-be^{2x} \right )= 0

 


Option 1)

y=ae^{x}-be^{2x}

Option 2)

y=ae^{x}+be^{2x}

Option 3)

y=ae^{x}+b

Option 4)

y=mx+c

Posted by

Himanshu

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