Question

To solve first order linear differential equation, we use following steps
(i) Write the solution of the given differential equation as
$y( IF )=\int(Q \times IF ) d x+C$
(ii) Write the given differential equation in the form $\frac{d y}{d x}+P y=Q$, where $P$ and $Q$ are constants or functions of $x$ only.
(iii) Find the integrating factor $( IF )=e^{\int P d x}$.
The correct order of the above steps is

• A. (ii), (iii), (i)
• B. (ii), (i), (iii)
• C. (iii), (i), (ii)
• D. (i), (iii), (ii)

Answer 1

Answer: (A)

Steps involved to solve first order linear differential equation.
(i) Write the given differential equation in the form $\frac{d y}{d x}+P y=Q$
where $P, Q$ are constants or functions of $x$ only.
(ii) Find the Integrating Factor (IF) $=e^{\int P d x}$.
(iii) Write the solution of the given differential equation as
$y(F)=\int(Q \times I F) d x+C$
Note In case, the first order linear differential equation is in the form $\frac{d x}{d y}+P_1 x=Q_1$, where $P_1$ and $Q_1$ are constants or functions of $y$ only. Then, IF $= e ^{\int \text { Rdy }}$ and the solution of the differential equation is given by
$x \cdot( IF )=\int\left(Q_1 \times IF \right) d y+C$