If m, n are the order and degree of the differential equation \(\left(\frac{d^{4} y}{d x^{4}}+\frac{d^{2} y}{d x^{2}}\right)^{\frac{1}{2}}=a \frac{d^{3} y}{d x^{3}}\) respectively, then the value of 4m - n is __________

The order and degree of the differential equation \(e^{\frac{d^{3}y}{d x^{2}}}+\cos (x) \frac{d y}{d x}=4 \text { is }\)__________

The order and degree of the differential equation \(\frac{d^{3} y}{d x^{3}}+6 \frac{d y}{d x}+3 y=0 \text { is }\)__________

The solution of the \(\operatorname{DE} \ y \frac{d x}{d y}=\cot x \text { is }\) __________

The solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is __________

The differential equation associated with the family of concentric circles having their centres at the origin is _________.

The I.F. of (1+y²) dx = (tan^-1-t-x) dy is ________.

Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

The differential equation of x²y = k is _________.

The general solution of x \(\frac{dy}{dx}\) = y is _________.

The solution of log \(\left( \frac { dy }{ dx } \right) \) = ax + by is______.

The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

On finding the differential equation corresponding to y = e^mx where m is the arbitrary constant, then m is ________.

The differential equation corresponding to xy = c² where c is an arbitrary constant is ________.

The order and degree of y'+(y")² = (x + t")² are _________.