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Linear Differential Equations

Form 102156.png + Py = Q, where P, Q are functions of x alone. For solving such equation we multiply both sides by integrating factor IF = 102150.png.
Solution of such differential equation 102143.png = 102136.png.
In some cases a linear differential equation may be of the form 103121.pngwhere P1 and Q1 are functions of y alone or constants. In such a case the integrating factor is 102130.png, and the solution is given by x. 102124.png = 102118.png .

Differential equation reducible to the linear form

Equation of the form:
f′(y)102112.png + f(y) P(x) = Q(x)  ...(4)
Put f(y) = u f′(y) 102106.png = 102100.png
Then (4) reduces to du/dx + uP(x) = Q(x), which is of the linear differential equation form.

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