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प्रश्न
The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______
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उत्तर
y = 1 – log x
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संबंधित प्रश्न
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Function y = ex + 1
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Solve the following differential equation.
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Solve
`dy/dx + 2/ x y = x^2`
`xy dy/dx = x^2 + 2y^2`
Solve the following differential equation
`yx ("d"y)/("d"x)` = x2 + 2y2
Solve the following differential equation
sec2 x tan y dx + sec2 y tan x dy = 0
Solution: sec2 x tan y dx + sec2 y tan x dy = 0
∴ `(sec^2x)/tanx "d"x + square` = 0
Integrating, we get
`square + int (sec^2y)/tany "d"y` = log c
Each of these integral is of the type
`int ("f'"(x))/("f"(x)) "d"x` = log |f(x)| + log c
∴ the general solution is
`square + log |tan y|` = log c
∴ log |tan x . tan y| = log c
`square`
This is the general solution.
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.
Solve the differential equation
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