Math Assignment Class XII Ch - 09
Differential Equations
Extra questions of chapter 09 Differential Equations, class XII with answers and hints to the difficult questions, strictly according to the CBSE Board syllabus. Important and useful math. assignment for the students of class XII
MATHEMATICS ASSIGNMENT OF EXTRA QUESTION
STRICTLY ACCORDING TO THE PREVIOUS CBSE SAMPLE QUESTION PAPERS AND CBSE BOARD PAPERS
Question: 1 If m and n, respectively, are the order and the degree of the differential equation
, then find m + n
Ans: 3
Solution Hint: Solve the above differential we get
Here m = 2 and n = 1 so m + n = 3
Question: 2 Write the order of the differential equation:
=\left%20(%20\frac{dy}{dx}%20\right%20)^{3}+x)
Answer: 2
Question: 3 Find the general solution of the differential equation 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0
Answer: y = C x
Question: 4 Solve the differential equation: ydx + (x – y2)dy
= 0
Answer:
Solution Hint: Reduce it to LDE and then solve it
Question: 5 Solve the differential equation:
Answer:
Solution Hint: Reduce it to HDE and then solve it
Question: 6
Find the general solution of the differential equation
Answer:
Solution Hint: Reduce the given equation into HDE and then solve it.
Question: 7
Find the particular solution of the following differential equation, given that y = 0 when x = π/4
Answer:
Solution Hint: Convert the given differential equation in LDE
Find Integrating Factor (IF) = sin x
Multiply by integrating factor on both side and then integrating we get
Now putting y = 0 when x = π/4 and find C, the value of C is given by
)
Now require particular solution is
%20\right%20]-\left%20(%20\frac{\pi%20}{2}+2tan\frac{\pi%20}{8}%20\right%20))
Question: 8
Write the general solution of differential equation
Answer: ex +e-y = C
Solution Hint: Given differential equation can be written as
Separating the denominator we get 
Integrating on both side we get:
⇒ ex +e-y = C
Question : 9 Find the particular solution of the following differential equation
siny\:%20dy=0;\:%20\:%20\:%20y(0)=\frac{\pi%20}{4})
Answer: 
Solution Hint: Use variable separable and integrating on both side we get
=log\:%20cosy+logC)
Now putting x = 0 and y = π/4 we get
C = 3√2
Now particular solution is given by
Question:10 Find the general solution of the differential equation:
Answer: xy sin y = sin y - y cos y + C
Solution Hint:
Separating the variables we get LDE shown below
IF = y sin y
Multiplying on both side by IF and then integrating we get
x.y sin y = sin y - y cos y + C
Question: 11
Find the particular solution of the differential equation : yexdx=(y3 + 2xey)dy , At y(0) = 1
Answer: x = - y2e-y + y2/e
Solution Hint: Given equation can be written as
It is Linear Differential Equation in x
Integrating Factor = 1/y2.
Multiply on both side by I.F. and then integrating we get
x = - y2e-y + Cy2.
Now putting x = 0 and y = 1, we get, C = 1/e
So particular solution is: x = - y2e-y + y2/e
Question 12
Show that (x - y)dy = (x + 2y)dx is a homogenous differential equation. Also,
find the general solution of the given differential equation.
Answer: -2\sqrt{3}tan^{-1}\left%20(%20\frac{2y+x}{\sqrt{3}x}%20\right%20)=C)
Solution Hint: Given differential equation can be written as
It is a Homogeneous differential equation. So solving it by making the substitution y/x = v and then integrating we get general solution
Question 13
Find the value of (2a - 3b), if a and b
represent respectively the order and the degree of the differential equation.
Answer: - 5
Order = 2 and Degree = 3
⇒ a = 2 and b = 3
2a - 3b = 2 × 2 - 3 × 3 = 4 - 9 = - 5
Question 14
Solve the differential equation (ex + 1)y dy = ex(y + 1)dx
Answer: log (ex
+ 1) = y - log(y + 1) + C
Question 15
Solve the following homogeneous differential equation : 
Answer: y = x ( log |x| + C )
Question 16Solve the differential equation )
Solution Hint
Write this equation in the standard form given equation reduces to HDE
Now putting y/x = v and integrating on both side we get

log sin v = - log x + log C
=\frac{C}{x}\:%20\:%20\Rightarrow%20\:%20\:%20xsin\left%20(%20\frac{y}{x}%20\right%20)=C)
Question: 17 Solve the following differential equation
Solution Hint: Simplify this equation we get
This is Linear Differential Equation
Finding IF and then integrating on both sides we get
Question: 18: Find the particular solution of the following differential equation.ex tan y dx + (2 - ex) sec2y dy = 0, given that y = π/4 when x = 0
Solution Hint: Separate the variables we get

Integrating on both side we get ex
– 2 = C tan y
Now putting y = π/4 and x = 0 we get C = -1
Required particular solution is
y = tan-1(2 + ex )
Question: 19: Solve the followings differential equation
, given that x = 1 at y = π/2
Solution Hint:
Reduce this equation into HDE and then putting y/x = v we get
Now integrating on both side and putting v = y/x we get
Now putting x = 1 and y = π/2 we get C = 0
Required solution of the given differential equation is
=log|x|)
Question: 20: Solve the following differential equations
, given that x = 0 at y = 1
Solution Hint:
Simplify the differential equation we get
(x+1)}dx)
Now integrating on both sides and by using the partial fraction we get
When x = 0, y = 1 we get C = 1
Question 21
Form the differential equation of all circles which is touching the x-axis at the origin.
Solution Hint
Equation of circle with centre C(0, r) and radius r is given by
(x - 0)2 + (y - 0)2 = r2
x2 + y2 = 2ry ........(i)
Differentiating w.r.t. x we get
2x + 2yy' = 2ry'
From this equation find the value of r and putting this value in equation (i) we get
(x2 + y2)y' = 2y(x + yy’)
This is the required differential equation
Question 22Find the differential equation of the family of curves y2 = 4ax
Ans: 2xyy' - y2 = 0
Question 23Find the solution of the differential equation
Solution Hint: Separate the variables and the integrating we get:
2e2y = x4 + C1
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