Advertisements
Advertisements
Question
Correct substitution for the solution of the differential equation of the type `("d"x)/("d"y) = "g"(x, y)` where g(x, y) is a homogeneous function of the degree zero is x = vy.
Options
True
False
Solution
This statement is True.
Explanation:
Since particular solution of a differential equation has no arbitrary constant.
APPEARS IN
RELATED QUESTIONS
Solve `sin x dy/dx - y = sin x.tan x/2`
Solve the differential equation `sin^(-1) (dy/dx) = x + y`
\[\frac{dy}{dx}\] + y cot x = x2 cot x + 2x
Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.
The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.
Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?
Solve the differential equation: (x + 1) dy – 2xy dx = 0
Solve the differential equation: (1 + x2) dy + 2xy dx = cot x dx
Solve the following differential equation :
`"dy"/"dx" + "y" = cos"x" - sin"x"`
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.
Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.
Solve the differential equation:
`"dy"/"dx" = 2^(-"y")`
If α, β are different values of x satisfying the equation a cos x + b sinα x = c, where a, b and c are constants, then `tan ((alpha + beta)/2)` is
`int cos(log x) dx = F(x) + C` where C is arbitrary constant. Here F(x) =
Find the general solution of the differential equation: (x3 + y3)dy = x2ydx
If y = y(x) is the solution of the differential equation `(1 + e^(2x))(dy)/(dx) + 2(1 + y^2)e^x` = 0 and y(0) = 0, then `6(y^'(0) + (y(log_esqrt(3))))^2` is equal to ______.
Let y = y(x) be the solution of the differential equation, `(2 + sinxdy)/(y + 1) (dy)/(dx)` = –cosx. If y > 0, y(0) = 1. If y(π) = a, and `(dy)/(dx)` at x = π is b, then the ordered pair (a, b) is equal to ______.
The solution of the differential equation `(1 + y^2) + (x - e^(tan^-1y)) (dy)/(dx)` = 0, is ______.
