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STD 12 - 9. differential equations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 9. differential equations4 Marks
MCQ
The difference between degree and order of a differential equation that represents the family of curves given by $y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right), a>0$ is
  • A
    $4$
  • B
    $3$
  • C
    $4$
  • ✓
    $2$
✓

Answer

Correct option: D.
$2$
d
$y ^{2}= a \left( x +\frac{\sqrt{ a }}{2}\right)= ax +\frac{ a ^{3 / 2}}{2}$ $...(1)$

$\Rightarrow 2 yy ^{\prime}= a$

put in equation (1)

$y^{2}=\left(2 y y^{\prime}\right) x+\frac{\left(2 y y^{\prime}\right)^{3 / 2}}{2}$

$\left(y^{2}-2 x y y^{\prime}\right)=\frac{\left(2 y y^{\prime}\right)^{3 / 2}}{2}$

squaring

$\left( y ^{2}-2 xyy ^{\prime}\right)^{2}=\frac{ y ^{3}\left( y ^{\prime}\right)^{3}}{2}$

$\therefore$ order $=1$

degree $=3$ Degree $=3-1=2$

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