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Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
Concept: undefined >> undefined
Concept: undefined >> undefined
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Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.
Concept: undefined >> undefined
Find the differential equation of the ellipse whose major axis is twice its minor axis.
Concept: undefined >> undefined
Find the differential equation of all circles having radius 9 and centre at point (h, k).
Concept: undefined >> undefined
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
Concept: undefined >> undefined
Form the differential equation of all parabolas whose axis is the X-axis.
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `(sin^-1 "x")^2 + "c"; (1 - "x"^2) ("d"^2"y")/"dx"^2 - "x" "dy"/"dx" = 2`
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = xm; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`
Concept: undefined >> undefined
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`
Concept: undefined >> undefined
Solve the following differential equation:
`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`
Concept: undefined >> undefined
Solve the following differential equation:
`log ("dy"/"dx") = 2"x" + 3"y"`
Concept: undefined >> undefined
Solve the following differential equation:
`"y" - "x" "dy"/"dx" = 0`
Concept: undefined >> undefined
Solve the following differential equation:
`"sec"^2 "x" * "tan y" "dx" + "sec"^2 "y" * "tan x" "dy" = 0`
Concept: undefined >> undefined
Solve the following differential equation:
cos x . cos y dy − sin x . sin y dx = 0
Concept: undefined >> undefined
Solve the following differential equation:
`"dy"/"dx" = - "k",` where k is a constant.
Concept: undefined >> undefined
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 0
Concept: undefined >> undefined
