Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
Which of the following is a second order differential equation?
Among the given options, the differential equation y′ y″ + y = sin x is the only one that involves the second derivative (y″), making it a second order differential equation. Thus, the correct answer is: y′ y″ + y = sin x Click here for more: https://www.tiwariacademy.com/ncert-solutions/class-12/maRead more
Among the given options, the differential equation
y′ y″ + y = sin x
is the only one that involves the second derivative (y″), making it a second order differential equation.
Thus, the correct answer is: y′ y″ + y = sin x
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-9
Solution of the differential equation 2x dx – 5y dy = 0 represents
Starting with the differential equation: 2x dx − 5y dy = 0 Separate variables: 2x dx = 5y dy Integrate both sides: ∫ 2x dx = ∫ 5y dy x² = (5/2)y² + C Rearrange the equation: x² − (5/2)y² = C This represents a family of conic sections. Since the equation is of the form: (x²) − (constant)·(y²) = C itRead more
Starting with the differential equation:
2x dx − 5y dy = 0
Separate variables:
2x dx = 5y dy
Integrate both sides:
∫ 2x dx = ∫ 5y dy
x² = (5/2)y² + C
Rearrange the equation:
x² − (5/2)y² = C
This represents a family of conic sections. Since the equation is of the form:
(x²) − (constant)·(y²) = C
it represents a family of hyperbolas (for nonzero C).
Thus, the correct answer is a hyperbola.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-9
The compound FeS is not attracted by magnet because
(d) FeS does not possess magnetic properties. https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-2/
(d) FeS does not possess magnetic properties.
https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-2/
See lessIf cos²x is an integrating factor of the differential equation dy/dx + Py = Q, then P can be
Given the differential equation: dy/dx + P y = Q The integrating factor μ(x) is defined by: μ(x) = exp(∫ P dx) We are told that: μ(x) = cos²x Taking the natural logarithm of both sides: ln μ(x) = ln(cos²x) = 2 ln|cos x| Differentiate with respect to x: d/dx [ln μ(x)] = d/dx [2 ln|cos x|] = 2 · (−tanRead more
Given the differential equation:
dy/dx + P y = Q
The integrating factor μ(x) is defined by:
μ(x) = exp(∫ P dx)
We are told that:
μ(x) = cos²x
Taking the natural logarithm of both sides:
ln μ(x) = ln(cos²x) = 2 ln|cos x|
Differentiate with respect to x:
d/dx [ln μ(x)] = d/dx [2 ln|cos x|] = 2 · (−tan x) = −2 tan x
But we also have:
d/dx [ln μ(x)] = P
Thus, we find:
P = −2 tan x
Therefore, the correct answer is:
−2 tan x
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-9
The order of the differential equation of family of parabolas whose axes are parallel to y-axis is
The family of parabolas with axes parallel to the y-axis can be expressed as: y = a x² + b x + c which contains three arbitrary constants, all of them, namely a, b, and c. A differential equation must therefore have a general solution containing three arbitrary constants. Three successive differentiRead more
The family of parabolas with axes parallel to the y-axis can be expressed as:
y = a x² + b x + c
which contains three arbitrary constants, all of them, namely a, b, and c.
A differential equation must therefore have a general solution containing three arbitrary constants. Three successive differentiations eliminate all the arbitrary constants. Indeed three successive differentiations of:
y = a x² + b x + c
After this gives:
y′ = 2a x + b
which twice gives:
y″ = 2a
and thrice gives:
y‴ = 0
So the differential equation that represents the family is:
y‴ = 0
This is a third order differential equation.
Thus, the order of the differential equation is 3.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-9