Answer to Question #91474 in Differential Equations for Sajid

Question

Q. Choose the correct answer
Q. Which of the following differential equation (with dependent variable y) are linear
(i) (x+y)dy=x2dx+y2dy
(ii) (x2+y)dy=x2dx+ydy
(iii)(x2+y)dy=sin ydx

Answer 1

(II)

First order linear differential equation has the form

$$\frac{dy}{dx}+P(x)y=Q(x)$$

Dividing the giving equations by dx, we can have the beforementioned form only in the 2nd case

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

$$x^2\frac{dy}{dx}+y\frac{dy}{dx}-y\frac{dy}{dx}=x^2$$ $$x^2\frac{dy}{dx}=x^2$$

$$\frac{dy}{dx}=1$$