Advertisements
Advertisements
प्रश्न
Obtain the differential equations by eliminating arbitrary constants from the following equation.
`y = c_2 + c_1/x`
उत्तर
`y = c_2 + c_1/x`
Differentiating w.r.t. x, we get
`dy/dx = (-c_1)/x^2`
∴ `x^2dy/dx = - c_1`
Again, differentiating w.r.t. x, we get
`x^2 (d^2y)/dx^2 + dy/dx. 2x = 0`
∴ `x^2 (d^2y)/dx^2 + 2x dy/dx = 0`
APPEARS IN
संबंधित प्रश्न
Form the differential equation by eliminating arbitrary constants from the relation `y=Ae^(5x)+Be^(-5x)`
Obtain the differential equation by eliminating the arbitrary constants from the following equation :
`y = c_1e^(2x) + c_2e^(-2x)`
If y = ae5x + be-5x then the differential equation is _________.
Obtain the differential equation by eliminating arbitrary constants from the following equations.
y = (c1 + c2 x) ex
Obtain the differential equations by eliminating arbitrary constants from the following equations.
y = c1e 3x + c2e 2x
Obtain the differential equation by eliminating arbitrary constants from the following equation.
y2 = (x + c)3
The differential equation by eliminating arbitrary constants from bx + ay = ab is __________.
Solve the differential equation:
Find the differential equation of family of curves y = ex (ax + bx2), where A and B are arbitrary constants.
State whether the following statement is True or False:
Number of arbitrary constant in the general solution of a differential equation is equal to order of D.E.
Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex
Obtain the differential equation by eliminating arbitrary constants from the following equation:
y = Ae3x + Be–3x
