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The general solution of the differential equation 

(y^{2}-x^{3})dx-xydy=0\: \: (x\neq 0) is : 

( where c is a constant of integration)

 

  • Option 1)

    y^{2}-2x^{2}+cx^{3}=0

  • Option 2)

    y^{2}+2x^{3}+cx^{2}=0

  • Option 3)

    y^{2}+2x^{2}+cx^{3}=0

  • Option 4)

    y^{2}-2x^{3}+cx^{2}=0

 

Answers (1)

general solution of the differential equation 

(y^{2}-x^{3})dx-xydy=0\: \: (x\neq 0)

=>y(ydy-xdy)=x^{3}dx

=>\frac{y}{x}(\frac{ydx-xdy}{x^{2}})=dx

=>-\frac{y}{x}d(\frac{y}{x})=dx

=>-\frac{1}{2}(\frac{y}{x})^{2}=x+k

=>-y^{2}=2x^{3}+2x^{2}k

=>y^{2}+2x^{3}+Cx^{2}=0


Option 1)

y^{2}-2x^{2}+cx^{3}=0

Option 2)

y^{2}+2x^{3}+cx^{2}=0

Option 3)

y^{2}+2x^{2}+cx^{3}=0

Option 4)

y^{2}-2x^{3}+cx^{2}=0

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