maple_dsolve.mws

>   

>    restart:

>   

>    with(DEtools):

>    dsolve(D(y)(x)=y(x)+(y(x))^3);  #  y' = y + y^3 - general solution

y(x) = 1/((-1+exp(-2*x)*_C1)^(1/2)), y(x) = -1/((-1+exp(-2*x)*_C1)^(1/2))

>    dsolve({ D(y)(x)=y(x)+(y(x))^3,  y(0)=2 } );  #  IVP with initial condition

y(x) = 1/((-1+5/4*exp(-2*x))^(1/2))

>    y(x) := 1/((-1+2*exp(-2*x)/exp(-2))^(1/2));

y(x) := 1/((-1+2*exp(-2*x)/exp(-2))^(1/2))

>    simplify(diff(y(x),x) - (y(x) + (y(x))^3));  # check DE by differentiating y(x)

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