To find the integral of
a d^{2}y/dx^{2} + b dy/dx + cy = XLet complementary function = Ay _{1} + By_{2},so that y _{1} and y_{2} satisfya d^{2}y/dx^{2} + b dy/dx + cy = 0Let us assume particular integral = uy _{1} + vy_{2},where u and v are unknown functions of x. Then, u = ∫[-y _{2}X/(y_{1}y'_{2} - y'_{1}y_{2})] dx;v = ∫[y _{1}X/(y_{1}y'_{2} - y'_{1}y_{2})] dx;General Solution = complementary function + particular integral. |

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