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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Differential Equations

NDA 2021 · Mathematics · Differential Equations

If the general solution of a differential equation is y^2+2 c y-c...

If the general solution of a differential equation is y2+2cy−cx+c2=0y^2+2 c y-c x+c^2=0, where cc is an arbitrary constant, then what is the order of the differential equation?

Options

  1. A11
  2. B22
  3. C33
  4. D44

Correct answer

B. 22

Step-by-step solution

y2+2cy−cx+c2=0y^2+2 c y-c x+c^2=02y⋅dydx+2c⋅dydx−c=02(dydx)2+2y⋅d2ydx2+2c⋅d2ydx2=0\begin{aligned} & 2 y \cdot \frac{d y}{d x}+2 c \cdot \frac{d y}{d x}-c=0 \\ & 2\left(\frac{d y}{d x}\right)^2+2 y \cdot \frac{d^2 y}{d x^2}+2 c \cdot \frac{d^2 y}{d x^2}=0\end{aligned}(y+c)⋅d2ydx2+2dydx(y+c) \cdot \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}
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