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Show that the lines \[\frac{5 - x}{- 4} = \frac{y - 7}{4} = \frac{z + 3}{- 5}\] and \[\frac{x - 8}{7} = \frac{2y - 8}{2} = \frac{z - 5}{3}\] are coplanar.
Concept: undefined >> undefined
Show that the lines \[\frac{x + 3}{- 3} = \frac{y - 1}{1} = \frac{z - 5}{5}\] and \[\frac{x + 1}{- 1} = \frac{y - 2}{2} = \frac{z - 5}{5}\] are coplanar. Hence, find the equation of the plane containing these lines.
Concept: undefined >> undefined
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Find the values of \[\lambda\] for which the lines
Concept: undefined >> undefined
If the lines \[x =\] 5 , \[\frac{y}{3 - \alpha} = \frac{z}{- 2}\] and \[x = \alpha\] \[\frac{y}{- 1} = \frac{z}{2 - \alpha}\] are coplanar, find the values of \[\alpha\].
Concept: undefined >> undefined
If the straight lines \[\frac{x - 1}{2} = \frac{y + 1}{k} = \frac{z}{2}\] and \[\frac{x + 1}{2} = \frac{y + 1}{2} = \frac{z}{k}\] are coplanar, find the equations of the planes containing them.
Concept: undefined >> undefined
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Concept: undefined >> undefined
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
Concept: undefined >> undefined
Show that y = C x + 2C2 is a solution of the differential equation \[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0.\]
Concept: undefined >> undefined
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Concept: undefined >> undefined
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Concept: undefined >> undefined
Find the differential equation corresponding to y = ae2x + be−3x + cex where a, b, c are arbitrary constants.
Concept: undefined >> undefined
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
Concept: undefined >> undefined
From x2 + y2 + 2ax + 2by + c = 0, derive a differential equation not containing a, b and c.
Concept: undefined >> undefined
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
Concept: undefined >> undefined
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
Concept: undefined >> undefined
\[\frac{dy}{dx} = y^2 + 2y + 2\]
Concept: undefined >> undefined
\[\frac{dy}{dx} + 4x = e^x\]
Concept: undefined >> undefined
\[\frac{dy}{dx} = x^2 e^x\]
Concept: undefined >> undefined
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
Concept: undefined >> undefined
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
Concept: undefined >> undefined
