निम्न में से कौनसी अवकल समीकरण रेखीय है ?

Question

Answer 1

(3) \(\frac1x\frac{d^2y}{dx^2}=e^x\)

⇒ \(\frac{d^2y}{dx^2}=xe^x\)

By comparing with \(\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x,y)=f(x),\)

we get p(x) = 0, q(x) = 0 f(x) = xe^x

∴ This is linear equation of second order.

(4) (xy² + x)dx + (y - x²y)dy = 0

⇒ \(\frac{dy}{dx} = \frac{xy^2+x}{x^2y-y}\) which is not a linear equation.