Final answer to the problem
$y=\sqrt{2\left(\ln\left(x\right)+c_0\right)}x,\:y=-\sqrt{2\left(\ln\left(x\right)+c_0\right)}x$
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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
We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $\frac{-y}{x}$ from both sides of the equation
$\frac{dy}{dx}=\frac{x}{y}-\frac{-y}{x}$
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$\frac{dy}{dx}=\frac{x}{y}-\frac{-y}{x}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx+(-y)/x=x/y. We need to isolate the dependent variable y, we can do that by simultaneously subtracting \frac{-y}{x} from both sides of the equation. Multiplying the fraction by -1. Multiply both sides of the equation by dx. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.
Final answer to the problem
$y=\sqrt{2\left(\ln\left(x\right)+c_0\right)}x,\:y=-\sqrt{2\left(\ln\left(x\right)+c_0\right)}x$
