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The order and degree of the differential equation whose solution is $\mathrm{y}=\mathrm{cx}+\mathrm{c}^{2}-3 \mathrm{c}^{3 / 2}+2$, where $\mathrm{c}$ is a parameter, is
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order $=1$, degree $=4$
$\mathrm{y}=\mathrm{cx}+\mathrm{c}^{2}-3 \mathrm{c}^{3 / 2}+2$ Differentiating above with respect to $x$, we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{c}$
Putting this value of $\mathrm{c}$ in (i), we get
$$
\mathrm{y}=\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}-3\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{3 / 2}+2
$$
Clearly its order is ONE and after removing the fractional power we get the degree FOUR.
Putting this value of $\mathrm{c}$ in (i), we get
$$
\mathrm{y}=\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}-3\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{3 / 2}+2
$$
Clearly its order is ONE and after removing the fractional power we get the degree FOUR.
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