Question Consider the differential equation dy/dx = y(y-5) with the initial condition y(0) = 1. Find y(1)
GL33AK The Asker · Calculus
Consider the differential equation dy/dx = y(y-5) with the initial condition y(0) = 1. Find y(1)
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{:[" Given: "(dy)/(dx)=y^(2)-5y],[=>(dy)/(y(y-5))=dx],[=>(1)/(5)[(1)/(y-5)-(1)/(y)]dy=dx],[:.((1)/(y-5)-(1)/(y))dy=5dx]:}Taking integration on both sido{:[=> ∣(dy)/(y+5)-int(dy)/(y)=int sdx],[=>ln |y-5|-ln |y|=5x+c]:}Now, y(0)=1{:[=>ln |1- ... See the full answer