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jms_zacher

  • 2 years ago

dy/dx = (y^2 + 2xy)/x^2 homogeneous diff equation

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  1. mukushla
    • 2 years ago
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    well in such equations u can start with letting \[z=\frac{y}{x}\]

  2. jms_zacher
    • 2 years ago
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    yeah i figured all of that part out. Its after integrating using partial fractions is where im stuck

  3. waleed_imtiaz
    • 2 years ago
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    ... Seperate the variables integrate them

  4. mukushla
    • 2 years ago
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    ok so u have \[z+x\frac{dz}{dx}=\frac{z^2x^2+2zx^2}{x^2}=z^2+2z\]\[x\frac{dz}{dx}=z^2+z\]and finally\[\frac{dz}{z(z+1)}=\frac{dx}{x}\]i think this is where u were stuck so just note that\[\frac{1}{z(z+1)}=\frac{1}{z}-\frac{1}{z+1}\]makes sense?

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