For each of the following differential equations verify that the accompanying function is a solution.
Differential equation
i. 
ii. 
iii. 
iv. 
v. 
Function
(i). The differential equation is
and the function to be proven as solution is y = ax, now we need to find the value of 
.
= a
Putting the value,
ax = y = ax,
As, L.H.S = R.H.S. the equation is satisfied, hence this function is the solution of the differential equation.
(ii). The differential equation is 
and the function to be proven as the solution of this equation is 
, now we need to find the value of 
.
Putting the values,
x – x = 0
As, L.H.S = R.H.S. the equation is satisfied, hence this function is the solution of the differential equation.
(iii). The differential equation is 
and the function to be proven as solution is
now we need to find the value of 
.
,
As L.H.S. ≠ R.H.S. the equation is not satisfied, hence this function is not the solution of this differential equation.
(iv). The differential equation is 
and the function to be proven as solution is 
, now we need to find the value of 
.
Putting the values,
,
As, L.H.S = R.H.S. the equation is satisfied, so hence this function is the solution of the differential equation.
(v). The differential equation is 
and the function to be proven as solution is 
, now we need to find the value of 
.
Putting the value, we get,
As, L.H.S = R.H.S. the equation is satisfied, so hence this function is the solution of the differential equation.