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- Exact Differential Equation
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We can identify that the differential equation $3\left(3x^2+y^2\right)dx-2xy\cdot dy=0$ 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
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$3\left(3x^2+y^2\right)dx-2xy\cdot dy=0$
Learn how to solve problems step by step online. Solve the differential equation 3(3x^2+y^2)dx-2xydy=0. We can identify that the differential equation 3\left(3x^2+y^2\right)dx-2xy\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. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.
