Advertisements
Advertisements
प्रश्न
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
उत्तर
We have,
\[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0\]
Now,y2 − x2 − xy = a
`rArr2y(dy)/(dx)-2x-y-x(dy)/(dx)=0`
`rArr(2y-x)(dy)/(dx)-2x-y=0`
`rArr(2y-x)(dy)/(dx)=2x+y`
`rArr(x-2y)(dy)/(dx)=-(2x+y)`
`rArr(x-2y)(dy)/(dx)+2x+y=0`
Thus, y2 − x2 − xy = a is the solution of the given differential equation.
APPEARS IN
संबंधित प्रश्न
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.
y2 = a (b2 – x2)
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 = e2x (a + bx)
Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.
Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
From x2 + y2 + 2ax + 2by + c = 0, derive a differential equation not containing a, b and c.
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
\[\frac{dy}{dx} + 4x = e^x\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
tan y dx + tan x dy = 0
(1 + x) y dx + (1 + y) x dy = 0
cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
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
Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?
The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is
The general solution of the differential equation `x^xdy + (ye^x + 2x) dx` = 0
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
The general solution of the differential equation y dx – x dy = 0 is ______.
Solve the differential equation: y dx + (x – y2)dy = 0
