Final answer to the problem
$\frac{dy}{dx}=\frac{x^2}{\left(y+1\right)^2\left(y\ln\left(x\right)\right)^{-1}}$
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Step-by-step Solution
1
Rewrite the differential equation using Leibniz notation
$\left(y\ln\left(x\right)\right)^{-1}\frac{dy}{dx}=\left(\frac{x}{y+1}\right)^2$
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$\left(y\ln\left(x\right)\right)^{-1}\frac{dy}{dx}=\left(\frac{x}{y+1}\right)^2$
Learn how to solve differential equations problems step by step online. . Rewrite the differential equation using Leibniz notation. 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}. Rewrite the differential equation. Divide fractions \frac{\frac{x^2}{\left(y+1\right)^2}}{\left(y\ln\left(x\right)\right)^{-1}} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
Final answer to the problem
$\frac{dy}{dx}=\frac{x^2}{\left(y+1\right)^2\left(y\ln\left(x\right)\right)^{-1}}$