Differential Equations
Order + degree sum
Grade Class 12
Question:
<p>If order \\(=m\\) and degree \\(=n\\) for \\(\\left(\\dfrac{d^2y}{dx^2}\\right)^3+\\left(\\dfrac{dy}{dx}\\right)^4+y^5=0\\), find \\(m+n\\).</p>
Step-by-Step Solution
Key Concept: Integer/Numeric entry — compute exact numerical answer.
<div class='solution'><p>Highest derivative: $d^2y/dx^2$ → order = 2. Power of highest derivative: 3 → degree = 3. $m+n = 2+3=5$. Answer: <strong>5</strong>.</p></div>
Correct Answer: 5