For the differential equation √(d^2ydx^2)=ydydx+xsindydx^23

Correct answer: (D) Order is 2 and degree is not defined. √(d^2ydx^2)=ydydx+xsindydx^23 ⇒d2ydx2^12=ydydx+xsindydx^23 ⇒d2ydx2^3=ydydx+xsindydx^4 Order of the differential equation is 2 and degree is not defined.

Q119 / 160 · TS EAMCET 2022 (18 Jul Shift 2) · Mathematics

For the differential equation $\sqrt{\frac{d^{2} y}{d x^{2}}} = \sqrt[3]{{[y \frac{d y}{d x} + x \sin (\frac{d y}{d x})]}^{2}}$

A
Order is $2$ and degree is $3$
B
Order is $3$ and degree is $3$
C
Order is $3$ and degree is $2$
Correct answer
D
Order is $2$ and degree is not defined

Solution

$\sqrt{\frac{d^{2} y}{d x^{2}}} = \sqrt[3]{{[y \frac{d y}{d x} + x \sin (\frac{d y}{d x})]}^{2}}$
$\Rightarrow {(\frac{d^{2} y}{d x^{2}})}^{\frac{1}{2}} = {[y \frac{d y}{d x} + x \sin (\frac{d y}{d x})]}^{\frac{2}{3}}$
$\Rightarrow {(\frac{d^{2} y}{d x^{2}})}^{3} = {[y \frac{d y}{d x} + x \sin (\frac{d y}{d x})]}^{4}$
Order of the differential equation is $2$ and degree is not defined.

Hence, the correct answer is option: 'D'.

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For the differential equation d2ydx2=ydydx+xsindydx23

Solution

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For the differential equation $\sqrt{\frac{d^{2} y}{d x^{2}}} = \sqrt[3]{{[y \frac{d y}{d x} + x \sin (\frac{d y}{d x})]}^{2}}$