Question #223861

Find the complete integral of p3 +q^3 = 27z.

Expert's answer

Let "u= x+ay" where a is an arbitrary constant. Replacing p by "\\frac{dz}{du}" and q by "a\\frac{dz}{du}"

"(\\frac{dz}{du})^3+(a\\frac{dz}{du})^3= 27 z\\\\\n(\\frac{dz}{du})^3+a^3(\\frac{dz}{du})^3= 27 z\\\\\n(1+a^3)(\\frac{dz}{du})=27z\\\\\n\\frac{1+a^3}{z}dz = 27u\\\\\nIntegrating \\\\\n(1+a^3)Log \\space z= 27 u +b\\\\\n(1+a^3)Log \\space z= 27 (x+ay) +b\\\\"

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