Well I have an initial value problem:
y+ dy/dx -xy^3=0, y(0)=2
So I've been working on this and below is my attempt (please tell me if im doing it right). Also I have no idea what to do with the condition of y(0)=2
dy/dx +y=xy^3
Where IF is of the form
dy/dx+Py=Q so this means p=1, Q=xy^3
so
e^ integral (Pdx) =e^integral(1dx) = e^x
solution is given by
y= Integral (Q(I.F.) dx
=integral (x(y^3)*e^x dx
y^3 Integral (x(e^x) dx)
y/y^3 =x(e^x) -e^x +c
So what do I do now? How do I solve the rest of it with the condition? Thank you for all of your time.
y+ dy/dx -xy^3=0, y(0)=2
So I've been working on this and below is my attempt (please tell me if im doing it right). Also I have no idea what to do with the condition of y(0)=2
dy/dx +y=xy^3
Where IF is of the form
dy/dx+Py=Q so this means p=1, Q=xy^3
so
e^ integral (Pdx) =e^integral(1dx) = e^x
solution is given by
y= Integral (Q(I.F.) dx
=integral (x(y^3)*e^x dx
y^3 Integral (x(e^x) dx)
y/y^3 =x(e^x) -e^x +c
So what do I do now? How do I solve the rest of it with the condition? Thank you for all of your time.