Advertisements
Advertisements
Question
The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
The given differential equation is `("d"y)/("d"x) = (y/x)^(1/3)`
⇒ `("d"y)/("d"x) = y^(1/3)/x^(1/3)`
⇒ `("d"y)/y^(1/3) = ("d"x)/x^(1/3)`
Integrating both sides, we get
`int ("d"y)/y^(1/3) = int ("d"x)/x^(1/3)`
⇒ `int y^(-1/3) "d"y = int x^(-1/3) "d"x`
⇒ `1/(- 1/3 + 1) y^(-1/3 + 1) = 1/(-1/3 + 1) * x^(-1/3) "d"x`
⇒ `1/(- 1/3 + 1) y^(-1/3 + 1) = 1/(-1/3 + 1) * x^(-1/3 + 1) + "c"`
⇒ `3/2 y^(2/3) = 3/2 x^(2/3) + "c"`
⇒ `y^(2/3) = x^(2/3) + 2/3 "c"`
⇒ `y^(2/3) - x^(2/3) = "k"["k" = 2/3 "c"]`
APPEARS IN
RELATED QUESTIONS
The differential equation of `y=c/x+c^2` is :
(a)`x^4(dy/dx)^2-xdy/dx=y`
(b)`(d^2y)/dx^2+xdy/dx+y=0`
(c)`x^3(dy/dx)^2+xdy/dx=y`
(d)`(d^2y)/dx^2+dy/dx-y=0`
The solution of the differential equation dy/dx = sec x – y tan x is:
(A) y sec x = tan x + c
(B) y sec x + tan x = c
(C) sec x = y tan x + c
(D) sec x + y tan x = c
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = x2 + 2x + C : y′ – 2x – 2 = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
Find the particular solution of the differential equation
`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is
Which of the following differential equations has y = x as one of its particular solution?
\[\frac{dy}{dx} = \left( x + y \right)^2\]
(x + y − 1) dy = (x + y) dx
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\left( 1 + y^2 \right) + \left( x - e^{- \tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- `y log y dx − x dy = 0`
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]
For the following differential equation, find a particular solution satisfying the given condition:- \[\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
y = aemx+ be–mx satisfies which of the following differential equation?
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
