Advertisements
Advertisements
Question
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
Options
yex = cos x + c
yex + ex cos x = c
yex = ex cos x + c
y2ex = ex cos x + c
Advertisements
Solution
yex = ex cos x + c
Hint:
`"dy"/"dx" + "y" = cos "x" - sin "x"`
I.F. = `"e"^(int 1 "dx") = "e"^"x"`
∴ the solution is `"y" * "e"^"x" = int (cos "x" - sin "x")"e"^"x" + "c"`
∴ yex = ex cos x + c
APPEARS IN
RELATED QUESTIONS
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
Ax2 + By2 = 1
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = A cos (log x) + B sin (log x)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y2 = (x + c)3
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
c1x3 + c2y2 = 5
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
In the following example verify that the given expression is a solution of the corresponding differential equation:
xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = xm; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`
Solve the following differential equation:
`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`
Solve the following differential equation:
cos x . cos y dy − sin x . sin y dx = 0
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 0
Solve the following differential equation:
`2"e"^("x + 2y") "dx" - 3"dy" = 0`
Reduce the following differential equation to the variable separable form and hence solve:
`("x - y")^2 "dy"/"dx" = "a"^2`
Reduce the following differential equation to the variable separable form and hence solve:
`cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"`
Reduce the following differential equation to the variable separable form and hence solve:
(2x - 2y + 3)dx - (x - y + 1)dy = 0, when x = 0, y = 1.
Solve the following differential equation:
(x2 + y2)dx - 2xy dy = 0
Choose the correct option from the given alternatives:
The differential equation of y = `"c"^2 + "c"/"x"` is
Choose the correct option from the given alternatives:
x2 + y2 = a2 is a solution of
The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.
Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
`"y"^2 = "a"("b - x")("b + x")`
Solve the following differential equation:
`"dy"/"dx" = "x"^2"y" + "y"`
Solve the following differential equation:
`"dy"/"dx" = ("2y" - "x")/("2y + x")`
Solve the following differential equation:
`"dy"/"dx" + "y cot x" = "x"^2 "cot x" + "2x"`
Solve the following differential equation:
`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`
Find the particular solution of the following differential equation:
`("x + 2y"^2) "dy"/"dx" = "y",` when x = 2, y = 1
Find the particular solution of the following differential equation:
(x + y)dy + (x - y)dx = 0; when x = 1 = y
Find the particular solution of the following differential equation:
y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2
Select and write the correct alternative from the given option for the question
Solution of the equation `x ("d"y)/("d"x)` = y log y is
Select and write the correct alternative from the given option for the question
General solution of `y - x ("d"y)/("d"x)` = 0 is
Find the differential equation of family of all ellipse whose major axis is twice the minor axis
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Form the differential equation of all straight lines touching the circle x2 + y2 = r2
Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis
The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.
The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.
Solve the following differential equation:
`xsin(y/x)dy = [ysin(y/x) - x]dx`
If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.
The differential equation of the family of circles touching Y-axis at the origin is ______.
Solve the differential equation
cos2(x – 2y) = `1 - 2dy/dx`
If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m2y2
Form the differential equation whose general solution is y = a cos 2x + b sin 2x.
Find the particular solution of the differential equation `x^2 dy/dx + y^2 = xy dy/dx`, if y = 1 when x = 1.
Solve the differential equation
ex tan y dx + (1 + ex) sec2 y dy = 0
Form the differential equation of all concentric circles having centre at the origin.
A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.
