If a second order differential equation is missing a dependant or independant variable, it can be reduced to a first order differential equation using substitution and solved using first order methods .

Dependant variable missing

If the dependent variable, y, is missing, make the substitution

{y'=p=\frac{dy}{dx}, y''=p'=\frac{dp}{dx}}

Independant variable missing

If the independent variable, x, is missing, make the substitution

{y'=p=\frac{dy}{dx}, y''=p'=\frac{dp}{dx}=\frac{dp}{dy}\frac{dy}{dx}=p\frac{dp}{dy}}

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