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Rinoa92 Rinoa92
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12 years ago
How do I solve this linear differential equation with variable substitution?

y'-y=xy^2 , with the substitution y(x)= 1/v(x).

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8kjw38kjw3
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12 years ago
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12 years ago
this is a bernoulli eq. withp(x)=-1

q(x)=x

N=2

y^-1=v


y^-2(dy/dx)=-dv/dx


reduces to: dv/dx+v=-x

itergration factor is e^ ?dx=e^x

then ve^x=- ?xe^xdx=

-xe^x+e^x+c

y^-1e^x=xe^x+e^x+c

or

1/y=-x+1+Ce^-x
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