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Y3dy/DX+y2+x=0 solve

Y3dy/DX+y2+x=0 solve

Grade:12

1 Answers

Kumar
37 Points
5 years ago
Given the differential equation y^3 * dy/dx + y^2 + x = 0.
Let us assume taht y^2 = v => 2y* dy/dx = dv/dx, using it in above equation reduce in following form i.e.
v * dv/dx +v =-x which solution is v=c/x^2 +2 x/3, where c is arbitrary canstant.
 Then the required solution is
y^2=c/x^2 +2 x/3.

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