Maths · Ordinary differential equations, their order and degree
The differential equation corresponding to where is an arbitrary constant, is:
The differential equation corresponding to \( x y=c^{2}, \) where \( c \) is an arbitrary constant, is:
- A. \( x y^{\prime \prime}+x=0 \)
- B. \( y^{\prime \prime}=0 \)
- C. \( x y^{\prime}+y=0 \)
- D. \( x y^{\prime \prime}-x=0 \)
Step-by-step solution
Given x y = c^2, differentiate both sides w.r.t. x: d/dx(xy) = d/dx(c^2) => y + x y' = 0, which is the required differential equation.
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