what is the differential equation of y ln x dx/dy=((y+1)/x)^2
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This is separable. That is all the "x" parts and all the "y" parts can be put on opposite sides
y ln x dx/dy = (y+1)² / x²
=> x² ln x dx = (y+1)²/y dy
=> x² ln x dx = ( y + 2 + 1/y ) dy
=> (1/9) x³ ( 3 ln x - 1 ) = (1/2) y² + 2y + ln |y| + C
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