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प्रश्न
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
उत्तर
`"x"("dy")/("dx")+"y"=3"x"^2-2`
⇒ `("dy")/("dx")+1/"x" . "y"=3"x"-2/"x""`
which is linear in y
`"I.F" : e ^(int 1/"x""dx") = e^log"x" ="x"`
General solution is :
`"y.x"= int(3"x"^2-2)"dx"`
`"xy" = "x"^3-2"x"+"C"`
⇒ `"y" = "x"^2-2+"C"/"x"`
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