Final answer to the problem
$\frac{y}{-x}+3\ln\left|\frac{x}{y}\right|=\ln\left|y\right|+C_0$
Step-by-step Solution
How should I solve this problem?
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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
Math interpretation of the question
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$\left(y^2+3xy\right)dx=\left(4x^2+xy\right)dy$
Learn how to solve problems step by step online. \left(y^2 + 3 x y\right) dx = \left(4 x^2 + x y\right) dy. Math interpretation of the question. We can identify that the differential equation \left(y^2+3xy\right)dx=\left(4x^2+xy\right)dy 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: x=uy. Expand and simplify.
Final answer to the problem
$\frac{y}{-x}+3\ln\left|\frac{x}{y}\right|=\ln\left|y\right|+C_0$
