Final Answer
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Factor the numerator by $2$
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$\frac{dy}{dx}=\frac{2\left(2x^2+2x+1\right)}{2\left(y+1\right)}$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(4x^2+4x+2)/(2(y+1)). Factor the numerator by 2. Cancel the fraction's common factor 2. Rewrite the differential equation in the standard form M(x,y)dx+N(x,y)dy=0. The differential equation y+1dy-\left(2x^2+2x+1\right)dx=0 is exact, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and they satisfy the test for exactness: \displaystyle\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. In other words, their second partial derivatives are equal. The general solution of the differential equation is of the form f(x,y)=C.