Question
Download Solution PDFWhat is the degree of the following differential equation?
\(\rm x=\sqrt{1+\frac{d^2y}{dx^2}}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Order of a differential equation is the highest order of derivative that occurs in the differential equation.
Degree of a differential equation is the highest power of the highest order derivative that occurs in the equation, after all the derivatives are converted into rational and radical free form.
Calculation:
Getting rid of the radicals by raising both the sides to power 2 will give us:
\(\rm x^2=1+(\frac{d^2y}{dx^2})^1\)
The highest derivative in it is \(\rm \frac{d^2y}{dx^2}\), therefore its order is 2.
∴ The highest power of this derivative in the equation is 1, therefore its degree is 1.
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