Maths · Ordinary differential equations, their order and degree

The order and degree of the differential equation. ^{3}+\left(\frac{d y}{d x}\ri

The order and degree of the differential equation. \( \left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)=\int y d x \) are respectively.

  • A. 2 and 3
  • B. 2 and 2
  • C. 3 \) and 1
  • D. 3 and 2

Step-by-step solution

The given equation includes an integral of y. Differentiating both sides with respect to x eliminates the integral and yields a third-order differential equation: 3(d^2y/dx^2)^2 (d^3y/dx^3) + (d^2y/dx^2) - y = 0. The highest derivative is d^3y/dx^3, so the order is 3. The highest derivative appears raised to the first power, so the degree is 1.
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