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प्रश्न
Solve: (x2 – yx2) dy + (y2 + xy2) dx = 0
उत्तर
Given differential equation is :
(x2 - yx2)dy + (y2 + xy2)dx = 0
⇒ x2(1-y)dy + y2 (1+x)dx = 0
⇒ `int(1-"y")/"y"^2 "dy" + int(1+"x")/"x"^2 "dx" = 0`
⇒ `int(1/"y"^2 - 1/"y")"dy" + int(1/"x"^2 + 1/"x")"dx" = 0`
⇒ `int"y"^-2"dy" - "log" "y" + int"x"^-2"dx" + "log x" = 0`
⇒ `"y"^-1/-1 - "log y" + "x"^-1/-1 + "log x" = C`
⇒ `-1/"y" - "log y" - 1/"x" + "log x" = C`
⇒ `- 1/"x" - 1/"y" + "log"("x"/"y") = C`
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