Advertisements
Advertisements
प्रश्न
Obtain the differential equation by eliminating arbitrary constants from the following equations.
y = Ae3x + Be−3x
उत्तर
y = Ae3x + B.e−3x ......(i)
Differentiating w.r.t. x, we get
`dy/dx = 3Ae^(3x) - 3 Be ^(-3x)`
Again, differentiating w.r. t. x, we get
`(d^2y)/dx^2 = 3A d/dxe^(3x) -3Bd/dx(e^(-3x))`
= `3A(3e^(3x)) - 3b(-3e^(-3x))`
=`9Ae^(3x)+9Be^(-3x)`
=`9(Ae^(3x)+Be^(-3x)) = 9y` ......[From(i)]
∴ `(d^2y)/dx^2 = 9y`
APPEARS IN
संबंधित प्रश्न
Form the differential equation by eliminating arbitrary constants from the relation `y=Ae^(5x)+Be^(-5x)`
If y = ae5x + be-5x then the differential equation is _________.
Obtain the differential equations by eliminating arbitrary constants from the following equation.
`y = c_2 + c_1/x`
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
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Form the differential equation by eliminating arbitrary constants from the relation
bx + ay = ab.
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
