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Solve the Differential Equation:"X"("D""Y")/("D""X")+"Y"=3"X"^2-2 - Mathematics

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Sum

Solve the differential equation:

`"x"("dy")/("dx")+"y"=3"x"^2-2`

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Solution

`"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"`

Concept: Basic Concepts of Differential Equation
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