Final answer to the problem
$y=\sqrt{x^{3}}-\sqrt{x}+\frac{2}{\sqrt{x}}+C_0$
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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
Rewrite the differential equation using Leibniz notation
Learn how to solve integrals of polynomial functions problems step by step online.
$\frac{dy}{dx}=\frac{\left(2x-1\right)\sqrt{x}-\frac{1}{2}x^{-\frac{1}{2}}\left(x^2-x+2\right)}{x}$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation y^'=((2x-1)x^(1/2)-1/2x^(-1/2)(x^2-x+2))/x. Rewrite the differential equation using Leibniz notation. Apply fraction cross-multiplication. Multiplying the fraction by x^{-\frac{1}{2}}\left(x^2-x+2\right). Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.
Final answer to the problem
$y=\sqrt{x^{3}}-\sqrt{x}+\frac{2}{\sqrt{x}}+C_0$
