The solution of frac{dy}{dx} = (x+y)^2 is | vedclass

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(A) To solve the differential equation $\frac{dy}{dx} = (x+y)^2$,we use the substitution method. Let $v = x+y$. Differentiating both sides with respec

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$	an^{-1}(x+y) = x+c$,where $c$ is the constant of integration

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(A) To solve the differential equation $\frac{dy}{dx} = (x+y)^2$,we use the substitution method. Let $v = x+y$. Differentiating both sides with respect to $x$,we get $\frac{dv}{dx} = 1 + \frac{dy}{dx}$,which implies $\frac{dy}{dx} = \frac{dv}{dx} - 1$. Substituting these into the original equation,we have $\frac{dv}{dx} - 1 = v^2$. Rearranging the terms,we get $\frac{dv}{dx} = 1 + v^2$. Separating the variables,we get $\frac{dv}{1+v^2} = dx$. Integrating both sides,we get $\int \frac{dv}{1+v^2} = \int dx$. This gives $	an^{-1}(v) = x + c$. Substituting $v = x+y$ back into the equation,we get $	an^{-1}(x+y) = x + c$.

The solution of $\frac{dy}{dx} = (x+y)^2$ is

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