# 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 P1 and Q1 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:

fâ€²(y) + f(y) P(x) = Q(x)  ...(4)

Put f(y) = u â‡’ fâ€²(y) =

Then (4) reduces to du/dx + uP(x) = Q(x), which is of the linear differential equation form.