Why Do We Use lP+mQ+nR=0 in the Solution of dx/P=dy/Q=dz/R?

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SUMMARY

The discussion centers on the mathematical expression lP + mQ + nR = 0, which is critical in solving the differential equation dx/P = dy/Q = dz/R. This equation is utilized to derive the integral form ldx + mdy + ndz = (lP + mQ + nR)dk = 0, where the condition lP + mQ + nR = 0 leads to an undefined or infinite expression. The participants clarify that this condition is essential for determining the relationship between the variables involved in the integration process.

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Dx/P = dy/Q = dz/R why we take lP+mQ+nR=0 and then solve?

why we take lP+mQ+nR = 0 in solution of dx/P=dy/Q=dz/R i-e ldx+mdy+ndz/(lP+mQ+nR) .. when lP+mQ+nR = 0 the expression goes to infinity .. how then we take integral of ldx+mdy+ndz as lx+my+nz= C. kindly clear
 
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Let the constant function be dk=dx/P = dy/Q = dz/R. Then we have
ldx+mdy+ndz= (lP+mQ+nR)dk = 0. Hence the solution.
 

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