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If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x
Concept: undefined >> undefined
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Determine the order and degree of the following differential equation:
`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 0`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
(y''')2 + 3y'' + 3xy' + 5y = 0
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`
Concept: undefined >> undefined
Evaluate the following integrals as limit of a sum : `""int_1^3 (3x - 4).dx`
Concept: undefined >> undefined
Evaluate the following integrals as limit of a sum:
`int _0^2 e^x * dx`
Concept: undefined >> undefined
Evaluate the following integrals as limit of a sum:
\[\int\limits_0^2 (3x^2 - 1)\cdot dx\]
Concept: undefined >> undefined
Evaluate the following integrals as limit of a sum : \[\int\limits_1^3 x^3 \cdot dx\]
Concept: undefined >> undefined
Evaluate the following integrals as limit of a sum:
\[\int\limits_0^4 x^2 \cdot dx\]
Concept: undefined >> undefined
Choose the correct option from the given alternatives:
The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`
Concept: undefined >> undefined
Determine the order and degree of the following differential equation:
`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`
Concept: undefined >> undefined
