Final answer to the problem
$\frac{3}{8}\ln\left|1+\frac{4y^2}{x^2}\right|=-\ln\left|x\right|+C_0$
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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Math interpretation of the question
$\left(x^2+y^2\right)dx+3xy\cdot dy=0$
Learn how to solve differential equations problems step by step online.
$\left(x^2+y^2\right)dx+3xy\cdot dy=0$
Learn how to solve differential equations problems step by step online. \left(\left(x^2\right) + \left(y^2\right)\right) dx + \left(3xy\right) dy = 0. Math interpretation of the question. We can identify that the differential equation \left(x^2+y^2\right)dx+3xy\cdot dy=0 is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, 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. Use the substitution: y=ux. Expand and simplify.
Final answer to the problem
$\frac{3}{8}\ln\left|1+\frac{4y^2}{x^2}\right|=-\ln\left|x\right|+C_0$
