Final answer to the problem
$\ln\left|y\right|-\frac{1}{2}\ln\left|y^2+1\right|=\frac{1}{2}\ln\left|x^2+1\right|+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Multiply the fraction by the term
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$\frac{1\left(x^2+1\right)}{x}\cdot dx=\left(y^3+y\right)dy$
Learn how to solve problems step by step online. Solve the differential equation 1/x(x^2+1)dx=(y^3+y)dy. Multiply the fraction by the term . Any expression multiplied by 1 is equal to itself. Divide both sides of the equation by dx. Simplify the fraction \frac{\frac{x^2+1}{x}dx}{dx} by dx.
Final answer to the problem
$\ln\left|y\right|-\frac{1}{2}\ln\left|y^2+1\right|=\frac{1}{2}\ln\left|x^2+1\right|+C_0$
