NCERT Solutions For Class 12 Maths Chapter 9 Differential Equations Ex 9.5

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5 Question Answer. I know many of you confuse about finding Chapter 9 Differential Equations Ex 9.5 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5

NCERT TEXTBOOK EXERCISES

Ex 9.5 Class 12 Maths Question 1.
(x²+xy)dy = (x²+y²)dx

Solution:

(x²+xy)dy = (x²+y²)dx

Ex 9.5 Class 12 Maths Question 2.
${ y }^{ I }=\frac { x+y }{ x }$

Solution:

${ y }^{ I }=\frac { x+y }{ x }$

Ex 9.5 Class 12 Maths Question 3.
(x-y)dy-(x+y)dx=0

Solution:

$\frac { dy }{ dx } =\frac { x+y }{ x-y } =\frac { 1+\frac { y }{ x } }{ 1-\frac { y }{ x } }$

Ex 9.5 Class 12 Maths Question 4.
(x²-y²)dx+2xy dy=0

Solution:

$\frac { dy }{ dx } =\frac { { y }^{ 2 }-{ x }^{ 2 } }{ 2xy }$

Ex 9.5 Class 12 Maths Question 5.
${ x }^{ 2 }\frac { dy }{ dx } ={ x }^{ 2 }-{ 2y }^{ 2 }+xy$

Solution:

$\frac { dy }{ dx } =1-2{ \left( \frac { y }{ x } \right) }^{ 2 }+\frac { y }{ x }$

Ex 9.5 Class 12 Maths Question 6.
$xdy-ydx=\sqrt { { x }^{ 2 }+{ y }^{ 2 } } dx$

Solution:

$xdy-ydx=\sqrt { { x }^{ 2 }+{ y }^{ 2 } } dx$

Ex 9.5 Class 12 Maths Question 7.
$\left{ xcos\left( \frac { y }{ x } \right) +ysin\left( \frac { y }{ x } \right) \right} ydx=\left{ ysin\left( \frac { y }{ x } \right) -xcos\left( \frac { y }{ x } \right) \right} xdy$

Solution:

$\left{ xcos\left( \frac { y }{ x } \right) +ysin\left( \frac { y }{ x } \right) \right} ydx=\left{ ysin\left( \frac { y }{ x } \right) -xcos\left( \frac { y }{ x } \right) \right} xdy$

Ex 9.5 Class 12 Maths Question 8.
$x\frac { dy }{ dx } -y+xsin\left( \frac { y }{ x } \right) =0$

Solution:

$x\frac { dy }{ dx } -y+xsin\left( \frac { y }{ x } \right) =0\Rightarrow \frac { dy }{ dx } =\frac { y }{ x } -sin\frac { y }{ x }$

Ex 9.5 Class 12 Maths Question 9.
$ydx+xlog\left( \frac { y }{ x } \right) dy-2xdy=0$

Solution:

$\frac { dy }{ dx } =\frac { y }{ 2x-xlog\frac { y }{ x } } =\frac { \frac { y }{ x } }{ 2-log\frac { y }{ x } }$

Ex 9.5 Class 12 Maths Question 10.
$\left( { 1+e }^{ \frac { x }{ y } } \right) dx+{ e }^{ \frac { x }{ y } }\left( 1-\frac { x }{ y } \right) dy=0$

Solution:

$\frac { dx }{ dy } =-\frac { { e }^{ \frac { x }{ y } }\left( 1-\frac { x }{ y } \right) }{ { 1+e }^{ \frac { x }{ y } } } =\frac { \left( \frac { x }{ y } -1 \right) { e }^{ \frac { x }{ y } } }{ { 1+e }^{ \frac { x }{ y } } } =f(x,y)$

For each of the following differential equation in Q 11 to 15 find the particular solution satisfying the given condition:

Ex 9.5 Class 12 Maths Question 11.
(x + y) dy+(x – y)dx = 0,y = 1 when x = 1

Solution:

given
(x + y) dy+(x – y)dx = 0

Ex 9.5 Class 12 Maths Question 12.
x²dy+(xy+y²)dx=0, y=1 when x=1

Solution:

$\frac { dy }{ dx } =\frac { xy+{ y }^{ 2 } }{ { x }^{ 2 } } =f(x,y)$
f(x,y) is homogeneous
∴ put y = vx

Ex 9.5 Class 12 Maths Question 13.
$\left( x{ sin }^{ 2 }\frac { y }{ x } -y \right) dx+xdy=0,y=\frac { \pi }{ 4 } ,when\quad x=1$

Solution:

$\left( x{ sin }^{ 2 }\frac { y }{ x } -y \right) dx+xdy=0$

Ex 9.5 Class 12 Maths Question 14.
$\frac { dy }{ dx } -\frac { y }{ x } +cosec\left( \frac { y }{ x } \right) =0,y=0\quad when\quad x=1$

Solution:

$\frac { dy }{ dx } -\frac { y }{ x } +cosec\left( \frac { y }{ x } \right) =0$
which is a homogeneous differential equation

Ex 9.5 Class 12 Maths Question 15.
$2xy-{ y }^{ 2 }-{ 2x }^{ 2 }\frac { dy }{ dx } =0,y=2,when\quad x=1$

Solution:

$\frac { dy }{ dx } =\frac { y }{ x } +\frac { 1 }{ 2 } { \left( \frac { y }{ x } \right) }^{ 2 }$ …(i)

Ex 9.5 Class 12 Maths Question 16.
A homogeneous equation of the form $\frac { dx }{ dy } =h\left( \frac { x }{ y } \right)$ can be solved by making the substitution,

(a) y=vx
(b) v=yx
(c) x=vy
(d) x=v

Solution:

(c) option x = vy

Ex 9.5 Class 12 Maths Question 17.
Which of the following is a homogeneous differential equation?

(a) (a) (4x + 6y + 5)dy-(3y + 2x + 4)dx = 0
(b) $(xy)dx-({ x }^{ 3 }+{ y }^{ 3 })dy$
(c) $({ x }^{ 3 }+{ 2y }^{ 2 })dx+2xydy=0$
(d) ${ y }^{ 2 }dx+{ (x }^{ 2 }-xy-{ y }^{ 2 })dy=0$

Solution:

(d)

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 PDF

For NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.5, you may click on the link below and get your NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise pdf file.