What is the solution for q^'(p)=(5400p^2q(p))/((p^3+2)^2) ?

The solution for q^'(p)=(5400p^2q(p))/((p^3+2)^2) is q(p)=e^{-(1800)/(p^3+2)+c_{1}}

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q^'(p)=(5400p^2q(p))/((p^3+2)^2)

q^{^{'}} (p) = \frac{5400 p ^{2} q ( p )}{( p ^{3} + 2 ) ^{2}}

q (p) = e^{- \frac{1800}{p ^{3} + 2} + c_{1}}

Solution steps

q^{'} (p) = \frac{5400 p ^{2} q ( p )}{( p ^{3} + 2 ) ^{2}}

Solve separable ODE:

q (p) = e^{- \frac{1800}{p ^{3} + 2} + c_{1}}

q (p) = e^{- \frac{1800}{p ^{3} + 2} + c_{1}}

What is the solution for q^'(p)=(5400p^2q(p))/((p^3+2)^2) ?
The solution for q^'(p)=(5400p^2q(p))/((p^3+2)^2) is q(p)=e^{-(1800)/(p^3+2)+c_{1}}