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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\frac{dy}{dx}=\frac{\left(2y+3\right)^2}{\left(4x+5\right)^2}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=((2y+3)/(4x+5))^2. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to . Solve the integral \int\frac{1}{\left(2y+3\right)^2}dy and replace the result in the differential equation.