Practicing Success
The differential equation whose solution is $A x^2+B y^2=1$, where A and B are arbitrary constants, is of |
second order and second degree first order and second degree first order and first degree second order and first degree |
second order and first degree |
We have, $A x^2+B y^2=1$ .....(i) Differentiating w.r. to $x$, we get $2 A x+2 B y \frac{d y}{d x}=0 \Rightarrow A x+B y \frac{d y}{d x}=0$ .......(ii) Differentiating w.r. to $x$, we get $A+B\left(\frac{d y}{d x}\right)^2+B y \frac{d^2 y}{d x^2}=0$ .....(iii) Multiplying (iii) by $x$ and subtracting (ii) from it, we get $x\left(\frac{d y}{d x}\right)^2+x y \frac{d^2 y}{d x^2}-y \frac{d y}{d x}=0$ Clearly, it is a second order and first degree differential equation. |