( ) . Here we have one independent variable. . .
Order and degree of a differential equation The highest order derivative present in the differential equation is the order of the differential equation. Degree is the highest power of the highest order derivative in the differential equation, after the equation has been cleared from fractions and the radicals as for as the derivatives are concerned. For example, consider the differential equation d y d y + + + Here the highest order derivatives is d y ( i.e 3rd order derivative). So the order of the differential equation is .
Now the power of highest order derivative d y is . ∴ The degree of the differential equation is . Example . Find the order and degree of the following differential equations.
(i) d y + + (ii) d y (iii) d y − + (iv) d y a d y (v) ′ + ′′