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GATE 2022 CE (CE1) – Question 12

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 1 mark · Multiple choice

For the equation $\frac{d^3y}{dx^3}+x\left(\frac{dy}{dx}\right)^{3/2}+x^2y=0$, the correct description is

  1. an ordinary differential equation of order 3 and degree 2.
  2. an ordinary differential equation of order 3 and degree 3.
  3. an ordinary differential equation of order 2 and degree 3.
  4. an ordinary differential equation of order 3 and degree 3/2.

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Show answer and explanation

Correct answer: (A) an ordinary differential equation of order 3 and degree 2.

Explanation

The highest derivative is $d^3y/dx^3$, so the order is 3. Isolate the fractional power and square: $(y\prime\prime\prime+x^2y)^2=x^2(y\prime)^3$.

The polynomial form has the highest-order derivative raised to power 2, so the degree is 2. **Answer: A.**