The equation of the form
dy/dx + Py = Qy^{n}where P and Q are constants or functions of x can be reduced to the linear form on dividing by y^{n} and substituting 1/y^{n-1} = zOn dividing both sides by y ^{n},(1/y^{n})(dy/dx) + (1/y^{n-1})P = Q.Put 1/y,^{n-1} = zso that [(1-n)/y^{n}]dy/dx = dz/dx∴ (1/(1-n))dz/dx + Pz = Qdz/dx + P(1-n)z = Q(1-n)Which is a linear equation and can be solved easily by the method discussed in the previous post. |

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