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- Exact Differential Equation
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- Integrate by partial fractions
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- FOIL Method
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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
Learn how to solve integrals of polynomial functions problems step by step online.
$L.C.M.=x^3$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy/dx=(y^3)/(x^3)+(-3y^2)/(x^2)(4y)/x+-1. 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. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Combine and simplify all terms in the same fraction with common denominator x^3. We can identify that the differential equation \frac{dy}{dx}=\frac{y^3-3y^2x+4yx^{2}-x^3}{x^3} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree.
