y=e^2x+x^2-yarcsin(1/x),求y′及dy

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y=e^2x+x^2-yarcsin(1/x),求y′及dy
y=e^2x+x^2-yarcsin(1/x),求y′及dy

y=e^2x+x^2-yarcsin(1/x),求y′及dy
y=e^2x+x^2-yarcsin(1/x)
y'=2e^2x+2x-y'arcsin(1/x)+y1/[x^2*√(1-1/x^2)]
y'={2e^2x+2x+y1/[x^2*√(1-1/x^2)]}/[1+arcsin(1/x)]
dy={2e^2x+2x+y1/[x^2*√(1-1/x^2)]}/[1+arcsin(1/x)]dx

y=e^2x+x^2-yarcsin(1/x)
y'=2e^2x+2x-y'arcsin(1/x)-y/√(1-1/x²)*(-1/x²)
y'+y'arcsin(1/x)=2e^2x+2x+y/x√(x²-1)
y'=[2e^2x+2x+y/x√(x²-1)]/[1+arcsin(1/x)]
dy=[2e^2x+2x+y/x√(x²-1)]/[1+arcsin(1/x)]dx