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Which of the following represents a particular solution of differential eqn \frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y= 0

  • Option 1)

    y=e^{x}-e^{2x}

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

best_answer

All A,B,C,D will be particular solution of some differential equation,but the one which satisfy given differential equation will be its particular solution ,On verifying we will see (A) will satisfy for (A)

y=e^{x}-e^{2x}\Rightarrow \frac{dy}{dx}= e^{x}-2e^{2x}\; and\: \frac{d^{2}y}{dx^{2}}= e^{x}-4e^{2x}

\therefore \frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y= \left ( e^{x}-4e^{2x} \right )-3\left ( e^{x}-2e^{2x} \right )+2\left ( e^{x}-e^{2x} \right )= 0


Option 1)

y=e^{x}-e^{2x}

Option 2)

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

Option 3)

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

Option 4)

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

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Himanshu

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