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NCERT Solutions For Class 12 Maths Chapter 9 Differential Equations Ex 9.3

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3 Question Answer. I know many of you confuse about finding Chapter 9 Differential Equations Ex 9.3 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 12
SubjectMaths
ChapterChapter 9
ExerciseClass 12 Maths Chapter 9 Differential Equations Exercise 9.3
Number of Questions Solved
NCERT Solutions For Class 12 Maths Chapter 9 Differential Equations Ex 9.3

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3

NCERT TEXTBOOK EXERCISES

Ex 9.3 Class 12 Maths Question 1.
$\frac { x }{ a } +\frac { y }{ b } =1$

Solution:

Given that $\frac { x }{ a } +\frac { y }{ b } =1$ …(i)
differentiating (i) w.r.t x, we get
$\frac { 1 }{ a } +\frac { 1 }{ b } { y }^{ I }=0$ …(ii)
again differentiating w.r.t x, we get
$\frac { 1 }{ b } { y }^{ II }=0\Rightarrow { y }^{ II }=0$
which is the required differential equation

Ex 9.3 Class 12 Maths Question 2.
y² = a(b² – x²)

Solution:

given that
y² = a(b² – x²)…(i)

Ex 9.3 Class 12 Maths Question 3.
y = ae3x+be-2x

Solution:

Given that
y = ae3x+be-2x …(i)

Ex 9.3 Class 12 Maths Question 4.
y = e2x (a+bx)

Solution:

y = e2x (a+bx)

Ex 9.3 Class 12 Maths Question 5.
y = ex(a cosx+b sinx)

Solution:

The curve y = ex(a cosx+b sinx) …(i)
differentiating w.r.t x

Ex 9.3 Class 12 Maths Question 6.
Form the differential equation of the family of circles touching the y axis at origin

Solution:

The equation of the circle with centre (a, 0) and radius a, which touches y- axis at origin

Ex 9.3 Class 12 Maths Question 7.
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Solution:

The equation of parabola having vertex at the origin and axis along positive y-axis is

Ex 9.3 Class 12 Maths Question 8.
Form the differential equation of family of ellipses having foci on y-axis and centre at origin.

Solution:

The equation of family ellipses having foci at y- axis is

Ex 9.3 Class 12 Maths Question 9.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.

Solution:

Equation of the hyperbola is $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1$
Differentiating both sides w.r.t x

which is the req. differential eq. of the hyperbola.

Ex 9.3 Class 12 Maths Question 10.
Form the differential equation of the family of circles having centre on y-axis and radius 3 units

Solution:

Let centre be (0, a) and r = 3
Equation of circle is
x² + (y – a)² = 9 …(i)
Differentiating both sides, we get

which is required equation

Ex 9.3 Class 12 Maths Question 11.
Which of the following differential equation has $y={ c }{ 1 }{ e }^{ x }+{ c }{ 2 }{ e }^{ -x }$ as the general solution ?

(a) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0$
(b) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$
(c) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +1=0$
(d) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -1=0$

Solution:

(b) $y={ c }{ 1 }{ e }^{ x }+{ c }{ 2 }{ e }^{ -x }\Rightarrow \frac { dy }{ dx } ={ c }{ 1 }{ e }^{ x }-{ c }{ 2 }{ e }^{ -x }$
$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ c }{ 1 }{ e }^{ x }+{ c }{ 2 }{ e }^{ -x }\Rightarrow \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$

Ex 9.3 Class 12 Maths Question 12.
Which of the following differential equations has y = x as one of its particular solution ?

(a) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -{ x }^{ 2 }\frac { dy }{ dx } +xy=x$
(b) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ x }\frac { dy }{ dx } +xy=x$
(c) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -{ x }^{ 2 }\frac { dy }{ dx } +xy=0$
(d) $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ x }\frac { dy }{ dx } +xy=0$

Solution:

(c) y = x
$\frac { dy }{ dx } =1,\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0$
$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -{ x }^{ 2 }\frac { dy }{ dx } +xy=0$

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.3 PDF

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