Order of differential equation of $y = m x + c$

Open in App

Solution

Eliminating arbitrary constants m and c from $y = m x + c .$
$\frac{d y}{d x} = m .$ Differentiating again, $\frac{d^{2} y}{d x^{2}} = 0 \dots (2)$ The two arbitrary constants have been eliminated and we have got a differential equation of second order.In the light of above we can say that if an equation contains n arbitrary constants, the result of elimination these constants will be a differential
equation of nth order. Equation (1)in ths above examples are called the General solution of
differential equation. Hence we can say that by solving a differential equation of nth order, we mean to find a relation between the two variables x,y and n independent arbitrary constants, such that when these constants are eliminated the given differential equation of nth order will be formed.

Suggest Corrections

Similar questions

y = {a e}^{m x} + {b e}^{- m x}

^{'} m^{'}

^{'} c^{'}

y = m x + c

D^{2} y - 3 D y - 4 y = - 4 x

y = a e^{b x + c}

a, b, c

y = m x

Join BYJU'S Learning Program