Solving Separable ODEs - Maple Help

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Solving Separable ODEs

Description

 • The general form of a separable ODE is given by the following:
 > separable_ode := diff(y(x),x)=f(x)*g(y(x));
 ${\mathrm{separable_ode}}{:=}\frac{{ⅆ}}{{ⅆ}{x}}{}{y}{}\left({x}\right){=}{f}{}\left({x}\right){}{g}{}\left({y}{}\left({x}\right)\right)$ (1)
 where f(x) and g(y) are arbitrary functions. See Differentialgleichungen, by E. Kamke, p. 15. This type of ODE can be solved in a general manner by dsolve.

Examples

 > $\mathrm{with}\left(\mathrm{DEtools},\mathrm{odeadvisor}\right)$
 $\left[{\mathrm{odeadvisor}}\right]$ (2)
 > $\mathrm{odeadvisor}\left(\mathrm{separable_ode}\right)$
 $\left[{\mathrm{_separable}}\right]$ (3)
 > $\mathrm{dsolve}\left(\mathrm{separable_ode}\right)$
 ${∫}{f}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{-}\left({{∫}}_{{}}^{{y}{}\left({x}\right)}\frac{{1}}{{g}{}\left({\mathrm{_a}}\right)}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_a}}\right){+}{\mathrm{_C1}}{=}{0}$ (4)
 See Also DEtools, odeadvisor, dsolve, and ?odeadvisor, where is one of: quadrature, linear, separable, Bernoulli, exact, homogeneous, homogeneousB, homogeneousC, homogeneousD, homogeneousG, Chini, Riccati, Abel, Abel2A, Abel2C, rational, Clairaut, dAlembert, sym_implicit, patterns; for other differential orders see odeadvisor,types.