A Short Course On Differential Equations

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An equation that does not contain x directly. Such an equation is of the form ^y'dx' 'dx")-''- CERTAIN PARTICULAR FORMS OF EQUATIONS 73 Let dy Then dx=^' d^y d / d^y dx^ "^ dx\ dx^ d^y dp dp dy dp ^ dx^ ^ dx~ dy dx ~ -^ dy * I dx \^ dy I dy \^ dy / dx dy' and so on.
The equation then becomes a differential equation in p and y of order n — 1. Suppose that it can be solved and that the solu- tion is^ z=f(y'). Then a solution of the original equation is 51. An equation which does not contain y dir
...ectly.
Such an equation is of the form Let dy The equation then becomes a differential equation in p and x of order n — 1. If the equation can be solved for p and the solution is^ =f(x), a solution of the original equation is 52. An equation of the first order solvable for y.
In such a case, when solved for y^ the equation becomes y=. F(x, p). (1) 6 74 SHORT COURSE ON DIFFERENTIAL EQUATIONS Differentiate with respect to x.
This equation does not contain y explicitly. It is an equation of the first order in p and x.


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