Advertisements
Advertisements
Question
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
x + y = tan–1y
⇒ `1 + "dy"/"dx" = 1/(1 + y^2) "dy"/"dx"`
⇒ `"dy"/"dx"(1/(1 + y^2) - 1)` = 1
i.e., `"dy"/"dx" = (-(1 + y^2))/y^2`
Which satisfies the given equation.
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
The differential equation of the family of curves y=c1ex+c2e-x is......
(a)`(d^2y)/dx^2+y=0`
(b)`(d^2y)/dx^2-y=0`
(c)`(d^2y)/dx^2+1=0`
(d)`(d^2y)/dx^2-1=0`
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y″ – y′ = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
xy = log y + C : `y' = (y^2)/(1 - xy) (xy != 1)`
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
Solve the differential equation `cos^2 x dy/dx` + y = tan x
Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
\[\frac{dy}{dx} - y \tan x = e^x \sec x\]
x2 dy + (x2 − xy + y2) dx = 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:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1
Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is `(2x)/y^2.`
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.
The solution of `x ("d"y)/("d"x) + y` = ex is ______.
The solution of the differential equation `("d"y)/("d"x) = "e"^(x - y) + x^2 "e"^-y` is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
