If A, B, C are three non-null square matrices of the same order, write the condition on A such that AB = AC⇒ B = C.
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
\[\frac{d^3 x}{d t^3} + \frac{d^2 x}{d t^2} + \left( \frac{dx}{dt} \right)^2 = e^t\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + 4y = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{dy/dx} = 2\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \left( c\frac{d^2 y}{d x^2} \right)^{1/3}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 + xy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\sqrt[3]{\frac{d^2 y}{d x^2}} = \sqrt{\frac{dy}{dx}}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{d^4 y}{d x^4} = \left\{ c + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x + \left( \frac{dy}{dx} \right) = \sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y\frac{d^2 x}{d y^2} = y^2 + 1\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x^2 \left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + y^4 = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Find the differential equation of all the parabolas with latus rectum '4a' and whose axes are parallel to x-axis.
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Show that the function y = A cos x + B sin x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + y = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Show that the function y = A cos 2x − B sin 2x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 4y = 0\].
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Show that y = AeBx is a solution of the differential equation
\[\frac{d^2 y}{d x^2} = \frac{1}{y} \left( \frac{dy}{dx} \right)^2\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
