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$4$
- ✓$2$
$\Rightarrow 2 yy ^{\prime}= a$
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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