Homogeneous Ordinary Differential Equations
Solve the following differential equations or Initial Value Problems (IVP).
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\(\displaystyle{\frac{dy}{dx} = \frac{y-x}{y+x}}\)
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\(\displaystyle{\frac{dy}{dx} = \frac{x^2+3y^2}{2xy}}\)
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\(\displaystyle{ -y \, dx + (x+\sqrt{xy})\, dy =0}\)
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\(\displaystyle{xy^2\frac{dy}{dx} = y^3-x^3, \quad y(1)=2}\)
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\(\displaystyle{(x^2+y^2)dx+(x^2-xy)dy =0 }\)
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\(\displaystyle{\frac{dy}{dx} = \frac{y-4x}{x-y}}\)
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