Advertisements
Advertisements
प्रश्न
The differential equation for which y = acosx + bsinx is a solution, is ______.
पर्याय
`("d"^2y)/("d"x^2) + y` = 0
`("d"^2y)/("d"x^2) - y` = 0
`("d"^2y)/("d"x^2) + ("a" + "b")y` = 0
`("d"^2y)/("d"x^2) + ("a" - "b")y` = 0
Advertisements
उत्तर
The differential equation for which y = acosx + bsinx is a solution, is `("d"^2y)/("d"x^2) - y` = 0.
Explanation:
The given equation is y = acosx + bsinx
`("d"y)/("d"x)` = – asinx + bcosx
`("d"^2y)/("d"x^2)` = – acosx – bsinx
⇒ `("d"^2y)/("d"x^2)` = – (acosx + bsinx)
⇒ `("d"^2y)/("d"x^2)` = –y
⇒ `("d"y)/("d"x) + y` = 0
APPEARS IN
संबंधित प्रश्न
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
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 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`
Find the particular solution of the differential equation `dy/dx=(xy)/(x^2+y^2)` given that y = 1, when x = 0.
Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`
Solve the differential equation `cos^2 x dy/dx` + y = tan x
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
(x2 + 1) dy + (2y − 1) dx = 0
(x3 − 2y3) dx + 3x2 y dy = 0
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
`x cos x(dy)/(dx)+y(x sin x + cos x)=1`
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
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
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.
Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.
`(dy)/(dx) + ycotx = 2/(1 + sinx)`
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
