Is $y=x^{2}+x$ a solution to $\frac{d y}{d x}=2\left(y-x^{2}\right)+1$ ?

Name: Is $y=x^{2}+x$ a solution to $\frac{d y}{d x}=2\left(y-x^{2}\right)+1$ ?
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Quizplus · Accepted Answer

To verify if $y=x^{2}+x$ is a solution, we differentiate $y$ with respect to $x$ to get $\frac{dy}{dx} = 2x + 1$. Substituting $y = x^2 + x$ into the given differential equation, we get $\frac{dy}{dx} = 2(x^2 + x - x^2) + 1 = 2x + 1$, which matches the derivative we found, confirming that $y=x^{2}+x$ is indeed a solution.

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Is $y=x^{2}+x$ A Solution To $\frac{d y}{d x}=2\left(y-x^{2}\right)+1$