- #1
courtrigrad
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Solve the equation [tex]\frac{dy}{dx}-y = -xe^{-2x}y^{3}[/tex].
So a Bernoulli differential equation is in the form [tex]\frac{dy}{dx} + P(x)y = Q(x)y^{n}[/tex]. Isn't the above equation in this form already?I set [tex]u = y^{-2}[/tex] and [tex]\frac{du}{dx} = -2y^{-3[/tex].
So [tex]-2y^{-3} + 2y^{-2} = 2xe^{-2x}[/tex]. From here what do I do?
Is the integrating factor [tex]I(x) = e^{\int -1 dx} = e^{-x}[/tex]?
Thanks
So a Bernoulli differential equation is in the form [tex]\frac{dy}{dx} + P(x)y = Q(x)y^{n}[/tex]. Isn't the above equation in this form already?I set [tex]u = y^{-2}[/tex] and [tex]\frac{du}{dx} = -2y^{-3[/tex].
So [tex]-2y^{-3} + 2y^{-2} = 2xe^{-2x}[/tex]. From here what do I do?
Is the integrating factor [tex]I(x) = e^{\int -1 dx} = e^{-x}[/tex]?
Thanks