Please select a subject first
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The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.
Concept: undefined >> undefined
Choose the correct option from the given alternatives:
The solution of the differential equation `"dy"/"dx" = sec "x" - "y" tan "x"`
Concept: undefined >> undefined
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The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.
Concept: undefined >> undefined
Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
Concept: undefined >> undefined
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
`"y"^2 = "a"("b - x")("b + x")`
Concept: undefined >> undefined
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`
Concept: undefined >> undefined
In the following example verify that the given function is a solution of the differential equation.
`"y" = "e"^"ax" sin "bx"; ("d"^2"y")/"dx"^2 - 2"a" "dy"/"dx" + ("a"^2 + "b"^2)"y" = 0`
Concept: undefined >> undefined
In the following example verify that the given function is a solution of the differential equation.
`"y" = 3 "cos" (log "x") + 4 sin (log "x"); "x"^2 ("d"^2"y")/"dx"^2 + "x" "dy"/"dx" + "y" = 0`
Concept: undefined >> undefined
In the following example verify that the given function is a solution of the differential equation.
`"xy" = "ae"^"x" + "be"^-"x" + "x"^2; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" + "x"^2 = "xy" + 2`
Concept: undefined >> undefined
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 = "2y"^2 log "y", "x"^2 + "y"^2 = "xy" "dx"/"dy"`
Concept: undefined >> undefined
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a sin (x + b)
Concept: undefined >> undefined
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = b(x + 4)
Concept: undefined >> undefined
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = `sqrt("a" cos (log "x") + "b" sin (log "x"))`
Concept: undefined >> undefined
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = `"Ae"^(3"x" + 1) + "Be"^(- 3"x" + 1)`
Concept: undefined >> undefined
Form the differential equation of all parabolas which have 4b as latus rectum and whose axis is parallel to the Y-axis.
Concept: undefined >> undefined
Form the differential equation of all the lines which are normal to the line 3x + 2y + 7 = 0.
Concept: undefined >> undefined
Form the differential equation of the hyperbola whose length of transverse and conjugate axes are half of that of the given hyperbola `"x"^2/16 - "y"^2/36 = "k"`.
Concept: undefined >> undefined
Solve the following differential equation:
`"dy"/"dx" = "x"^2"y" + "y"`
Concept: undefined >> undefined
Solve the following differential equation:
`"dy"/"dx" = ("2y" - "x")/("2y + x")`
Concept: undefined >> undefined
Solve the following differential equation:
x dy = (x + y + 1) dx
Concept: undefined >> undefined
