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Rewrite the differential equation using Leibniz notation
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$\frac{dy}{dx}=\frac{2-e^x}{3+2y}$
Learn how to solve problems step by step online. Solve the differential equation y^'=(2-e^x)/(3+2y). Rewrite the differential equation using Leibniz notation. Divide fractions \frac{1}{\frac{1}{3+2y}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Integrate both sides of the differential equation, the left side with respect to . Expand the integral \int\left(3+2y\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately.