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Simplify `cos theta[(cos theta, sintheta),(-sin theta, cos theta)] + sin theta[(sin theta, -cos theta), (cos theta, sin theta)]`
Concept: undefined >> undefined
Show that `[(5, -1),(6, 7)][(2, 1),(3, 4)] ≠ [(2, 1),(3, 4)][(5, -1),(6, 7)]`
Concept: undefined >> undefined
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Show that `[(1, 2, 3),(0, 1, 0),(1, 1, 0)][(-1, 1, 0),(0, -1, 1),(2, 3, 4)] ≠ [(-1, 1, 0),(0, -1, 1),(2, 3, 4)][(1, 2, 3),(0, 1, 0),(1, 1, 0)]`
Concept: undefined >> undefined
Find A2 – 5A + 6I, if A = `[(2, 0, 1),(2, 1, 3),(1, -1, 0)]`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
(x2 + xy) dy = (x2 + y2) dx
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`y' = (x + y)/x`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
(x – y) dy – (x + y) dx = 0
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
(x2 – y2) dx + 2xy dy = 0
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`x^2 dy/dx = x^2 - 2y^2 + xy`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`x dy - y dx = sqrt(x^2 + y^2) dx`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`{xcos(y/x) + ysin(y/x)}ydx = {ysin (y/x) - xcos(y/x)}xdy`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`x dy/dx - y + x sin (y/x) = 0`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`y dx + x log(y/x)dy - 2x dy = 0`
Concept: undefined >> undefined
Show that the given differential equation is homogeneous and solve them.
`(1+e^(x/y))dx + e^(x/y) (1 - x/y)dy = 0`
Concept: undefined >> undefined
For the differential equation find a particular solution satisfying the given condition:
(x + y) dy + (x – y) dx = 0; y = 1 when x = 1
Concept: undefined >> undefined
For the differential equation find a particular solution satisfying the given condition:
x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Concept: undefined >> undefined
For the differential equation find a particular solution satisfying the given condition:
`[xsin^2(y/x - y)] dx + x dy = 0; y = pi/4 "when" x = 1`
Concept: undefined >> undefined
For the differential equation find a particular solution satisfying the given condition:
`dy/dx - y/x + cosec (y/x) = 0; y = 0` when x = 1
Concept: undefined >> undefined
For the differential equation find a particular solution satisfying the given condition:
`2xy + y^2 - 2x^2 dy/dx = 0; y = 2` when x = 1
Concept: undefined >> undefined
A homogeneous differential equation of the from `dx/dy = h (x/y)` can be solved by making the substitution.
Concept: undefined >> undefined
