方程\((x + 2y){\rm{d}}x - x{\rm{d}}y = 0\)的通解是（ ）。
A: \(y = {x^2} - x\)
B: \(y = C{x^2} - x\)
C: \(y = C{x^2} +x\)
D: \(y = {x^2} +x\)
A: \(y = {x^2} - x\)
B: \(y = C{x^2} - x\)
C: \(y = C{x^2} +x\)
D: \(y = {x^2} +x\)
举一反三
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- 下列不等式正确的是（ ） A: \( { { {e^x} + {e^y}} \over 2} < {e^ { { {x + y} \over 2}}}\quad (x \ne y)\) B: \((x + y){e^{x + y}} < x{e^{2x}} + y{e^{2y}}\quad (x > 0,y > 0,x \ne y)\) C: \( { { {x^n} + {y^n}} \over 2} < {( { { x + y} \over 2})^n}\quad (x > 0,y > 0,x \ne y,n > 1)\) D: \(x\ln x + y\ln y < (x + y)ln { { x + y} \over 2}\quad (x > 0,y > 0,x \ne y)\)