Solve (2y + x) dy/dx = 1

Correct Answer is : x+2y+2=ceyx + 2y + 2 = ce^{y}x+2y+2=cey

Correct Answer is : x+2y+2=ceyx + 2y + 2 = ce^{y}x+2y+2=cey

Test Index

UPSC NDA Math Model Paper 7

Question : 80 of 120

Marks: +1, -0

Solve

(2y + x) \frac{dy}{dx} = 1

Solution:

The given equation is

(2y + x) \frac{dy}{dx} = 1

\Rightarrow (2y + x) = \frac{dy}{dx}

\Rightarrow \frac{dx}{dy} - x = 2y

∴ It is linear differential equation is of first order

\text{IF} = e^{\int -1 \, dy}

\Rightarrow \text{IF} = e^{-y}

Now,

x \times (\text{IF}) = \int Q (\text{IF}) \, dy

\Rightarrow x \times e^{-y} = \int 2y \times e^{-y} \, dy

\Rightarrow xe^{-y} = 2\left[ y \int e^{-y} \, dy \right.

- \int \left\{ \frac{dy}{dy} \times \int e^{-y} \, dy \right\} \, dy

\Rightarrow xe^{-y} = 2\left[ -ye^{-y} + \int e^{-y} \, dy \right] + c

\Rightarrow xe^{-y} = 2\left[ -ye^{-y} - e^{-y} \right] + c

\Rightarrow x + 2y + 2 = ce^{y}

Go to Question:

Prev Question

Next Question