Method of Variation of Parameters

To find the integral of  
a d2y/dx2 + b dy/dx + cy = X

Let complementary function = Ay1 + By2,
so that y1 and y2 satisfy
a d2y/dx2 + b dy/dx + cy = 0

Let us assume particular integral = uy1 + vy2,
where u and v are unknown functions of x.

Then, u = [-y2X/(y1y'2 - y'1y2)] dx;
v = [y1X/(y1y'2 - y'1y2)] dx;

General Solution = complementary function + particular integral.



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