I have a ordinary equation as" 2 times derivative of y w.r.t. x +square of x multiplied by cos y=0" Question is to tell whether it is linear or non linear.??
According to me since double derivative has degree 1 and also function of y has degree 1and no product of dependent function and any derivative seen .so it must be linear . But my text book says it is non linear . Plzzz correct me if i m wrong.
It seems like the equation you're dealing with is $$\frac{d^2y}{dx^2}+x^2\cos y=0.$$
Because the highest-order derivative occurring in the equation is a second derivative, it's a second-order equation. The most general form of a second-order linear ordinary differential equation is $$\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x)y=r(x),$$ where $p$, $q$, and $r$ can be any continuous functions of $x$. Notice that in that most general form, there are no functions of $y$ or of both $x$ and $y$, only of $x$. Therefore, the presence of $\cos y$ makes the entire equation non-linear.