# Linear Differential Equations

Form +

*Py*=*Q*, where*P*,*Q*are functions of*x*alone. For solving such equation we multiply both sides by integrating factor IF = .Solution of such differential equation = .

In some cases a linear differential equation may be of the form where

*P*_{1}and*Q*_{1}are functions of*y*alone or constants. In such a case the integrating factor is , and the solution is given by*x*. = .# Differential equation reducible to the linear form

Equation of the form:

*f*â€²(

*y*) +

*f*(

*y*)

*P*(

*x*) =

*Q*(

*x*) ...(4)

Put

*f*(*y*) =*u*â‡’*f*â€²(*y*) =Then (4) reduces to

*du*/*dx*+*uP*(*x*) =*Q*(*x*), which is of the linear differential equation form.