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Question
Solve the following differential equation:
`"dy"/"dx" = "x"^2"y" + "y"`
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Solution
`"dy"/"dx" = "x"^2"y" + "y"`
∴ `"dy"/"dx" = "y"("x"^2 + 1)`
∴ `1/"y" "dy" = ("x"^2 + 1)"dx"`
Integrating both sides, we get
`int 1/"y" "dy" = int ("x"^2 + 1)"dx"`
∴ `log |"y"| = "x"^3/3 + "x" + "c"`
This is the general solution.
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