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$\frac{dx}{dy}=\frac{\frac{1}{2}}{x+3}$
Learn how to solve problems step by step online. Solve the differential equation dx/dy=(1/2*1)/(x+3). Simplifying. Rewrite the differential equation in the standard form M(x,y)dx+N(x,y)dy=0. The differential equation x+3dx-\frac{1}{2}dy=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. Using the test for exactness, we check that the differential equation is exact.