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  • Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 20

Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 20

Answers (1)

Answer:

 The required differential equation is

\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=\frac{1}{y}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}

Hint:

 Differentiating the given equation with respect to x

Given:

 y=ae^{bx+5}

Solution:

y=ae^{bx+5} \qquad \qquad \dots(i)

Where a and b are arbitrary constants

Differentiating with respect to x

\frac{\mathrm{d} y}{\mathrm{d} x}=a.be^{bx+5} \qquad \qquad \dots (ii)

Again, Differentiating with respect to x

\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}=a.b^{2}e^{bx+5} \qquad \qquad \dots (iii)

Put

b=\frac{1}{y}\frac{\mathrm{d} y}{\mathrm{d} x}

from (i) and (ii) in equation (iii), we get

\frac{\mathrm{d}^{2}y }{\mathrm{d} x^{2}}=y.\frac{1}{y^{2}}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}

\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=\frac{1}{y}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}

 The required differential equation is

\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=\frac{1}{y}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}

Posted by

Gurleen Kaur

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