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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 _______.
Option: 1 2
Option: 2 3
Option: 3 1
Option: 4 0

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\\y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right)=a x+\frac{a^{3 / 2}}{2} \\ \text{differentiate both side } \\ \Rightarrow 2 y y^{\prime}=a \\\Rightarrow y^2=(2yy')x+\frac{(2yy')^{3/2}}{2}

\begin{aligned} &\left(y^{2}-2 x y y^{\prime}\right)=\frac{\left(2 y y^{\prime}\right)^{3 / 2}}{2}\\ &\text { squaring }\\ &\left(y^{2}-2 x y y^{\prime}\right)^{2}=\frac{y^{3}\left(y^{\prime}\right)^{3}}{2} \end{aligned}

Order = 1

Degree = 3

Posted by

himanshu.meshram

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