MHT CET · Maths · Differential Equations
If \(m\) and \(n\) are order and degree of the equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}-1\), then
- A \(m=3, n=3\)
- B \(m=3, n=2\)
- C \(m=3, n=5\)
- D \(m=3, n=1\)
Answer & Solution
Correct Answer
(B) \(m=3, n=2\)
Step-by-step Solution
Detailed explanation
The given differential equation can be rewritten as
\(
\begin{array}{l}
\left(\frac{d^{2} y}{d x^{2}}\right)^{5} \cdot \frac{d^{3} y}{d x^{3}}+4\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2} \\
=\left(x^{2}-1\right) \frac{d^{3} y}{d x^{3}} \Rightarrow \text { order }(m)=3
\end{array}
\)
and \(\quad\) degree \((n)=2\)
\(
\begin{array}{l}
\left(\frac{d^{2} y}{d x^{2}}\right)^{5} \cdot \frac{d^{3} y}{d x^{3}}+4\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d^{3} y}{d x^{3}}\right)^{2} \\
=\left(x^{2}-1\right) \frac{d^{3} y}{d x^{3}} \Rightarrow \text { order }(m)=3
\end{array}
\)
and \(\quad\) degree \((n)=2\)
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