Advertisements
Advertisements
Question
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Solution
y = e2x (a + bx) ...(1)
Differentiating both sides with respect to x, we get:
This is the required differential equation of the given curve.
APPEARS IN
RELATED QUESTIONS
Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = a e3x + b e– 2x
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = ex (a cos x + b sin x)
Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
Show that y = C x + 2C2 is a solution of the differential equation \[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Find the differential equation corresponding to y = ae2x + be−3x + cex where a, b, c are arbitrary constants.
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = y^2 + 2y + 2\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} = x^2 e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]
tan y dx + tan x dy = 0
cosec x (log y) dy + x2y dx = 0
(1 − x2) dy + xy dx = xy2 dx
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
Find the general solution of the following differential equation:
`x (dy)/(dx) = y - xsin(y/x)`
General solution of tan 5θ = cot 2θ is
The number of arbitrary constant in the general solution of a differential equation of fourth order are
The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is
The general solution of the differential equation `(ydx - xdy)/y` = 0
The general solution of the differential equation `x^xdy + (ye^x + 2x) dx` = 0
The general solution of the differential equation y dx – x dy = 0 is ______.
Solve the differential equation: y dx + (x – y2)dy = 0
