Advertisements
Advertisements
Question
A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution
Advertisements
Solution
particular
RELATED QUESTIONS
Verify that y2 = 4ax is a solution of the differential equation y = x \[\frac{dy}{dx} + a\frac{dx}{dy}\]
Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.
Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation
\[y - x\frac{dy}{dx} = y^2 + \frac{dy}{dx}\]
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
y2 dx + (x2 − xy + y2) dy = 0
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
Solve the following differential equation.
`dy/dx + 2xy = x`
The solution of `dy/ dx` = 1 is ______
Solve the differential equation:
`e^(dy/dx) = x`
Solve:
(x + y) dy = a2 dx
`dy/dx = log x`
Solve: `("d"y)/("d"x) + 2/xy` = x2
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
The function y = ex is solution ______ of differential equation
The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______
Solve the following differential equation `("d"y)/("d"x)` = cos(x + y)
Solution: `("d"y)/("d"x)` = cos(x + y) ......(1)
Put `square`
∴ `1 + ("d"y)/("d"x) = "dv"/("d"x)`
∴ `("d"y)/("d"x) = "dv"/("d"x) - 1`
∴ (1) becomes `"dv"/("d"x) - 1` = cos v
∴ `"dv"/("d"x)` = 1 + cos v
∴ `square` dv = dx
Integrating, we get
`int 1/(1 + cos "v") "d"v = int "d"x`
∴ `int 1/(2cos^2 ("v"/2)) "dv" = int "d"x`
∴ `1/2 int square "dv" = int "d"x`
∴ `1/2* (tan("v"/2))/(1/2)` = x + c
∴ `square` = x + c
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.
Solve the differential equation
`y (dy)/(dx) + x` = 0
