Advertisements
Advertisements
प्रश्न
Find the value of m so that the function y = emx solution of the given differential equation.
y’ + 2y = 0
Advertisements
उत्तर
y’ + 2y = 0 .......(1)
Given y = emx ........(2)
Differentiating equation (2) w.r.t x, we get
`("d"y)/("d"x)` = emx m
`("d"y)/("d"x)` = ym
`("d"y)/("d"x) - "m"y` = 0
`y"'"- "m"y` = 0 .........(3)
∴ Comparing equation (1) and (3)
We get m = – 2
APPEARS IN
संबंधित प्रश्न
Show the following expressions is a solution of the corresponding given differential equation.
y = 2x2 ; xy’ = 2y
Show the following expressions is a solution of the corresponding given differential equation.
y = aex + be–x ; y'' – y = 0
Find the value of m so that the function y = emx solution of the given differential equation.
y” – 5y’ + 6y = 0
Show that y = e–x + mx + n is a solution of the differential equation `"e"^x(("d"^2y)/("d"x^2)) - 1` = 0
Show that y = `"a"x + "b"/x ≠ 0` is a solution of the differential equation x2yn + xy’ – y = 0
Show that y = ae–3x + b, where a and b are arbitrary constants, is a solution of the differential equation `("d"^2y)/("d"x^2) + 3("d"y)/("d"x)` = 0
Show that the differential equation representing the family of curves y2 = `2"a"(x + "a"^(2/3))`, where a is a postive parameter, is `(y^2 - 2xy ("d"y)/("d"x))^3 = 8(y ("d"y)/("d"x))^5`
Choose the correct alternative:
The general solution of the differential equation `("d"y)/("d"x) = y/x` is
Choose the correct alternative:
The solution of the differential equation `2x ("d"y)/("d"x) - y = 3` represents
Choose the correct alternative:
The solution of the differential equation `("d")/("d"x) + 1/sqrt(1 - x^2) = 0` is
