Question
For each of the differential equations given below, indicate its order and degree (if defined). $\Big(\frac{\text{dy}}{\text{dx}}\Big)^3-4\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+7\text{y}=\sin\text{x}$
✓
Answer
Given: Differential equation $\Big(\frac{\text{dy}}{\text{dx}}\Big)^3-4\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+7\text{y}=\sin\text{x}$
The highest order derivative present in this differential equation is $\frac{\text{dy}}{\text{dx}}$ and hence order of this differential equation if 1.
The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{\text{dy}}{\text{dx}}$ is 3.
Therefore, order = 1, Degree = 3
The highest order derivative present in this differential equation is $\frac{\text{dy}}{\text{dx}}$ and hence order of this differential equation if 1.
The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{\text{dy}}{\text{dx}}$ is 3.
Therefore, order = 1, Degree = 3
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