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Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.
Concept: undefined >> undefined
The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (−1, 1).
Concept: undefined >> undefined
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Find the equation of the curve that passes through the point (0, a) and is such that at any point (x, y) on it, the product of its slope and the ordinate is equal to the abscissa.
Concept: undefined >> undefined
The x-intercept of the tangent line to a curve is equal to the ordinate of the point of contact. Find the particular curve through the point (1, 1).
Concept: undefined >> undefined
Define a differential equation.
Concept: undefined >> undefined
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Concept: undefined >> undefined
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
Concept: undefined >> undefined
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
Concept: undefined >> undefined
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
Concept: undefined >> undefined
Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]
Concept: undefined >> undefined
The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by
Concept: undefined >> undefined
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
Concept: undefined >> undefined
The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
Concept: undefined >> undefined
The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is
Concept: undefined >> undefined
The solution of the differential equation \[\frac{dy}{dx} = \frac{ax + g}{by + f}\] represents a circle when
Concept: undefined >> undefined
The solution of the differential equation \[\frac{dy}{dx} - \frac{y\left( x + 1 \right)}{x} = 0\] is given by
Concept: undefined >> undefined
The solution of the differential equation y1 y3 = y22 is
Concept: undefined >> undefined
The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is
Concept: undefined >> undefined
The differential equation satisfied by ax2 + by2 = 1 is
Concept: undefined >> undefined
Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]
Concept: undefined >> undefined
