Advertisements
Advertisements
Question
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.
Options
y = `(x^2 + "c")/(4x^2)`
y = `x^2/4 + "c"`
y = `(x^4 + "c")/x^2`
y = `(x^4 + "c")/(4x^2)`
Advertisements
Solution
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is y = `(x^4 + "c")/(4x^2)`.
Explanation:
I.F. = `"e"^(int 2/x "d"x) = "e"^(2logx)`
= `"e"^(logx^2)`
= x2.
Therefore, the solution is y.
x2 = `int x^2 * x "d"x`
= `x^4/4 + "k"`,
i.e., y = `(x^4 + "c")/(4x^2)`.
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`
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 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
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
Show that the general solution of the differential equation `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.
Solve the differential equation `cos^2 x dy/dx` + y = tan x
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
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.
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
(x3 − 2y3) dx + 3x2 y dy = 0
\[\frac{dy}{dx} + 5y = \cos 4x\]
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
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:
\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 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.
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 ______.
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
