Question

$\frac{dy}{dx}+x\sin y=\ln x$ is a linear differential equation of first order.

• A. True
• B. False

Answer 1

The correct option is B False

So it looks like a linear differential equation Right? But it is not. You are missing something. Here if you compare it to basic form of linear differential equation $\frac{dy}{dx}+P\left(x\right)y=Q\left(x\right)$ the second term $x\sin y$ is a misfit for L.D.E because we cannot have any transcendental functions of $y$ (dependent variable) in the equation. Nor we can have transcendental functions of $\frac{dy}{dx}$. So had it been $\sin \left(\frac{dy}{dx}\right)+xy=\ln x$ still it would not have been a linear differential equation.