Maths · Ordinary differential equations, their order and degree
Consider the following statements: 1. The general solution of + \) is of the for
Consider the following statements: 1. The general solution of \( \frac{d y}{d x}=f(x)+ \) \( x \) is of the form \( y=g(x)+c, \) where \( c \) is an arbitrary constant. 2. The degree of \( \left(\frac{d y}{d x}\right)^{2}=f(x) \) is 2 Which of the above statements is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Step-by-step solution
Statement 1: Integrating dy/dx = f(x) + x gives y = ∫f(x)dx + ∫x dx = g(x) + c, so correct. Statement 2: The highest derivative is dy/dx raised to power 2, so degree is 2, correct.
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