Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`2"e"^("x + 2y") "dx" - 3"dy" = 0`
Advertisements
उत्तर
`2"e"^("x + 2y") "dx" - 3"dy" = 0`
∴ `2"e"^"x" * "e"^"2y" "dx" - 3"dy" = 0`
∴ `2"e"^"x" "dx" - 3/"e"^"2y" "dy" = 0`
Integrating both sides, we get
`2 int "e"^"x" "dx" - 3 int "e"^(-2"y") "dy" = "c"_1`
∴ `2"e"^"x" - 3 * ("e"^(- "2y"))/(- 2) = "c"_1`
∴ `4"e"^"x" + 3"e"^(- 2"y") = 2"c"_1`
∴ `4"e"^"x" + 3"e"^(- 2"y") = "c"`, where c = 2c1.
This is the general solution.
APPEARS IN
संबंधित प्रश्न
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:
(y - a)2 = 4(x - b)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a + `"a"/"x"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = c1e2x + c2e5x
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = e−2x (A cos x + B sin x)
Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`
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:
cos x . cos y dy − sin x . sin y dx = 0
Solve the following differential equation:
`"dy"/"dx" = "e"^("x + y") + "x"^2 "e"^"y"`
For the following differential equation find the particular solution satisfying the given condition:
`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1
Reduce the following differential equation to the variable separable form and hence solve:
`"dy"/"dx" = cos("x + y")`
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 all circles having their centres on the line y = 5 and touching the X-axis is
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" = ("y" + sqrt("x"^2 - "y"^2))/"x"` is
Choose the correct option from the given alternatives:
The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`
In the following example verify that the given function is a solution of the differential equation.
`"y" = 3 "cos" (log "x") + 4 sin (log "x"); "x"^2 ("d"^2"y")/"dx"^2 + "x" "dy"/"dx" + "y" = 0`
In the following example verify that the given function is a solution of the differential equation.
`"xy" = "ae"^"x" + "be"^-"x" + "x"^2; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" + "x"^2 = "xy" + 2`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = a sin (x + b)
Form the differential equation of all parabolas which have 4b as latus rectum and whose axis is parallel to the Y-axis.
Solve the following differential equation:
`"dy"/"dx" = ("2y" - "x")/("2y + x")`
Solve the following differential equation:
`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`
Find the particular solution of the following differential equation:
`"dy"/"dx" - 3"y" cot "x" = sin "2x"`, when `"y"(pi/2) = 2`
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
Find the particular solution of the following differential equation:
`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`
Find the differential equation of family of lines making equal intercepts on coordinate axes
Find the general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`
Form the differential equation of y = (c1 + c2)ex
Find the differential equation from the relation x2 + 4y2 = 4b2
The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.
Find the differential equation of the family of all non-vertical lines in a plane
Find the differential equation of the family of parabolas with vertex at (0, –1) and having axis along the y-axis
Choose the correct alternative:
The slope at any point of a curve y = f(x) is given by `("d"y)/("d"x) - 3x^2` and it passes through (-1, 1). Then the equation of the curve is
The differential equation of all lines perpendicular to the line 5x + 2y + 7 = 0 is ____________.
The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.
The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.
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 all parabolas whose axis is Y-axis, 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
Solve the differential equation
ex tan y dx + (1 + ex) sec2 y dy = 0
