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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Differential Equations

NDA 2017 · Mathematics · Differential Equations

What is the general solution of the differential equation y d...

What is the general solution of the differential equation ydx−(x+2y2)dy=0y d x-\left(x+2 y^2\right) d y=0 ?

Options

  1. Ax=y2+cyx=y^2+c y
  2. Bx=2cy2\mathrm{x}=2 \mathrm{cy}{ }^2
  3. Cx=2y2+cyx=2 y^2+c y
  4. DNone of the above

Correct answer

C. x=2y2+cyx=2 y^2+c y

Step-by-step solution

ydx−(x+2y2)dy=0⇒ydx−xdy−2y2dy=0⇒y−x⋅dydx=2y2⋅dydx⇒y−x⋅dydxy2=2⋅dydx\begin{aligned} & y d x-\left(x+2 y^2\right) d y=0 \\ & \Rightarrow y d x-x d y-2 y^2 d y=0 \\ & \Rightarrow y-x \cdot \frac{d y}{d x}=2 y^2 \cdot \frac{d y}{d x} \\ & \Rightarrow \frac{y-x \cdot \frac{d y}{d x}}{y^2}=2 \cdot \frac{d y}{d x} \end{aligned} Integrating ⇒xy=2y+c⇒x=2y2+cy\begin{aligned} & \Rightarrow \frac{x}{y}=2 y+c \\ & \Rightarrow x=2 y^2+c y \end{aligned}
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