Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
A differential equation in which the dependent variable, say y, depends only on one independent variable, say x, is called as ordinary differential equation
विकल्प
True
False
Advertisements
उत्तर
True
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx = (1 - cos x)/(1+cos x)`
For the differential equation, find the general solution:
`dy/dx = (1+x^2)(1+y^2)`
For the differential equation, find the general solution:
`dy/dx = sin^(-1) x`
For the differential equation find a particular solution satisfying the given condition:
`(x^3 + x^2 + x + 1) dy/dx = 2x^2 + x; y = 1` When x = 0
For the differential equation find a particular solution satisfying the given condition:
`x(x^2 - 1) dy/dx = 1` , y = 0 when x = 2
Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = e x sin x.
The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.
In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 doubles itself in 10 years (loge 2 = 0.6931).
Find the particular solution of the differential equation:
`y(1+logx) dx/dy - xlogx = 0`
when y = e2 and x = e
Solve the equation for x:
sin-1x + sin-1(1 - x) = cos-1x, x ≠ 0
Solve the differential equation `"dy"/"dx" = 1 + "x"^2 + "y"^2 +"x"^2"y"^2`, given that y = 1 when x = 0.
Verify y = log x + c is a solution of the differential equation
`x(d^2y)/dx^2 + dy/dx = 0`
Solve the differential equation:
`dy/dx = 1 +x+ y + xy`
Solve `dy/dx = (x+y+1)/(x+y-1) when x = 2/3 and y = 1/3`
The resale value of a machine decreases over a 10 year period at a rate that depends on the age of the machine. When the machine is x years old, the rate at which its value is changing is ₹ 2200 (x − 10) per year. Express the value of the machine as a function of its age and initial value. If the machine was originally worth ₹1,20,000, how much will it be worth when it is 10 years old?
Solve
`y log y dx/ dy = log y – x`
Find the solution of `"dy"/"dx"` = 2y–x.
Solve the differential equation `(x^2 - 1) "dy"/"dx" + 2xy = 1/(x^2 - 1)`.
Solve the differential equation `"dy"/"dx" + 1` = ex + y.
Find the equation of the curve passing through the (0, –2) given that at any point (x, y) on the curve the product of the slope of its tangent and y-co-ordinate of the point is equal to the x-co-ordinate of the point.
Solve the following differential equation
x2y dx – (x3 + y3)dy = 0
