In the context of differential equation
Match List I with List II
|
LIST I |
LIST II |
||
| A. |
$\frac{dy}{dx}=\frac{1+y^2}{1+x^2}$ |
I. |
Not a differential equation |
| B. |
$x^2 \frac{dy}{dx}=x^2-2y^2+xy$ |
II. |
Linear first order |
| C. |
$sin x+y=cos(x+y)$ |
III. |
Variable separable |
| D. |
$(x+y)\frac{dy}{dx}=1$ |
IV. |
Homogenous |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
A. $\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$
$\Rightarrow \frac{1}{1+y^2} d y=\frac{1}{1+x^2} d x$
⇒ III variable separable
B. $x^2 \frac{d y}{d x} =x^2-2 y^2+x y$
$\frac{d y}{d x} =\frac{x^2}{x^2}-2\left(\frac{y}{x}\right)^2+\frac{x y}{x^2}$
$\frac{d y}{d x} =1-2(\frac{y}{x})^2+(\frac{y}{x})=f(\frac{y}{x})$
⇒ IV. Homogenous
C. sin x + y = cos (x + y)
⇒ I. Not a differential equation
D. $(x+y) \frac{d y}{d x}=1$
⇒ II. Linear first order