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Differential Equations by E. Rukmangadachari

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4

Differential Equations of the First Order but not of the First Degree

We will now discuss the solutions of differential equations which are of the first order but are of degree higher than one. Such differential equations will contain only the first order differential coefficient image but will occur in a degree higher than one. It is usual to denote image by p. The general form of such a differential equation is then

 

pn + A1 pn−1 + A2 pn−2 + … + An−1 p + An = 0

 

where A1, A2An are some functions of x and y.

Now we will consider various methods of ...

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