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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Differential Equations

NDA 2018 · Mathematics · Differential Equations

The equation of the curve passing through the point (-1,-2) which...

The equation of the curve passing through the point (−1,−2)(-1,-2) which satisfies dydx=−x2−1x3\frac{d y}{d x}=-x^2-\frac{1}{x^3} is

Options

  1. A17x2y−6x2+3x5−2=017 x^2 y-6 x^2+3 x^5-2=0
  2. B6x2y+17x2+2x5−3=06 x^2 y+17 x^2+2 x^5-3=0
  3. C6xy−2x2+17x5+3=06 x y-2 x^2+17 x^5+3=0
  4. D17x2y+6xy−3x5+5=017 x^2 y+6 x y-3 x^5+5=0

Correct answer

B. 6x2y+17x2+2x5−3=06 x^2 y+17 x^2+2 x^5-3=0

Step-by-step solution

dydx=−x2−1x3⇒∫dy=∫(−x2−1x3)dx⇒y=−x33+12x2+c\begin{aligned} & \frac{d y}{d x}=-x^2-\frac{1}{x^3} \\ & \Rightarrow \quad \int d y=\int\left(-x^2-\frac{1}{x^3}\right) d x \\ & \Rightarrow \quad y=-\frac{x^3}{3}+\frac{1}{2 x^2}+c \end{aligned} Putting (−1,−2)(-1,-2), we get −2=13+12+c⇒C=−176-2=\frac{1}{3}+\frac{1}{2}+c \Rightarrow \mathrm{C}=-\frac{17}{6}
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