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Factoring by $1+x^2$
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$\left(1+x^2\right)\left(dy+dx\right)=0$
Learn how to solve problems step by step online. Solve the differential equation (1+x^2)dy+(1+x^2)dx=0. Factoring by 1+x^2. Divide both sides of the equation by 1+x^2. Zero divided by anything is equal to zero. The differential equation dy+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.
