Advertisements
Advertisements
प्रश्न
Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0
y = `a + b/x`
`(dy)/(dx) = square`
`(d^2y)/(dx^2) = square`
Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`
= `x square + 2 square`
= `square`
Hence y = `a + b/x` is solution of `square`
Advertisements
उत्तर
`x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0
y = `a + b/x`
`("d"y)/("d"x)` = `bb((-b)/x^2)`
`(d^2y)/(dx^2)` = `bb((2b)/x^3)`
Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`
= `bb(x (2b)/x^3 + 2(-2)/x^2)`
= 0
Hence y = `a + b/x` is solution of `bb(x(d^2y)/(dx^2) + 2(dy)/(dx) = 0)`
संबंधित प्रश्न
Show that the function y = A cos x + B sin x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + y = 0\]
Show that the function y = A cos 2x − B sin 2x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 4y = 0\].
Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
Differential equation \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x
x cos2 y dx = y cos2 x dy
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?
If the marginal cost of manufacturing a certain item is given by C' (x) = \[\frac{dC}{dx}\] = 2 + 0.15 x. Find the total cost function C (x), given that C (0) = 100.
The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.
The tangent at any point (x, y) of a curve makes an angle tan−1(2x + 3y) with x-axis. Find the equation of the curve if it passes through (1, 2).
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
The solution of the differential equation y1 y3 = y22 is
The differential equation satisfied by ax2 + by2 = 1 is
Verify that the function y = e−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]
For each of the following differential equations find the particular solution.
`y (1 + logx)dx/dy - x log x = 0`,
when x=e, y = e2.
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.
The value of `dy/dx` if y = |x – 1| + |x – 4| at x = 3 is ______.
