The equation of the curve in which subnormal varies as the square of the ordinate is (\lambda is constant of the proportionality)

  • Option 1)

    y=Ce^{2 \lambda x}

  • Option 2)

    y=Ce^{\lambda x}

  • Option 3)

    y^{2}+\lambda x=c

  • Option 4)

    y^{2}+\lambda x^{2}=c

 

Answers (1)

Solution of Differential Equation -

\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )

put

 Z =ax+by+c

- wherein

Equation with convert to

\int \frac{dz}{bf\left ( z \right )+a} =x+c

 

 Length of subnormal is y\frac{dy}{dx}

It is given that y\frac{dy}{dx} = \lambda y ^{2}

\therefore \frac{dy}{dx}=\lambda y

\therefore\int \frac{dy}{dx}=\lambda \int dx

\therefore log y=\lambda x+C

\therefore y=e^{\lambda x+c}=e ^{\lambda x}.c

 


Option 1)

y=Ce^{2 \lambda x}

Incorrect

Option 2)

y=Ce^{\lambda x}

Incorrect

Option 3)

y^{2}+\lambda x=c

Incorrect

Option 4)

y^{2}+\lambda x^{2}=c

Incorrect

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