### Featured Posts

### Math Assignment Class XII Ch -09 | Differential Equations

- Get link
- Other Apps

# Math Assignment | Class XII

Differential Equations|Chapter 09

**Extra questions of chapter 09 Differential Equations, class XII with answers and hints to the difficult questions, strictly according to the CBSE Board syllabus.****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:**

**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 – y**

^{2})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**

**Question: 8**

**Write the general solution of differential equation**

**Answer: e**

^{x}+e^{-y}= C

**Solution Hint: Given differential equation can be written as**

**Separating the denominator we get**

**Integrating on both side we get:**

**⇒ e**

^{x}+e^{-y}= C**Question : 9 Find the particular solution of the following differential equation**

**Answer:**

**Solution Hint: Use variable separable and integrating on both side we get**

**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 : ye**

^{x}dx=(y^{3 }+ 2xe^{y})dy , At y(0) = 1

**Answer: x = - y**

^{2}e^{-y}+ y^{2}/e

**Solution Hint: Given equation can be written as**

**It is Linear Differential Equation in x**

**Integrating Factor = 1/y ^{2}.**

**Multiply on both side by I.F. and then integrating we get**

**x = - y ^{2}e^{-y} + Cy^{2}.**

**Now putting x = 0 and y = 1, we get, C = 1/e**

**So particular solution is: x = - y ^{2}e^{-y} + y^{2}/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:**

**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 (e**

^{x}+ 1)y dy = e^{x}(y + 1)dxAnswer: log (e^{x}
+ 1) = y - log(y + 1) + C

**Question 15**

**Solve the following homogeneous differential equation : **

**Answer: y = x ( log |x| + C )**

**Question 16**

Solve 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

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.

e^{x} tan y dx + (2 - e^{x}) sec^{2}y dy = 0, given that y = π/4 when x = 0

Solution Hint: Separate the variables we get

Integrating on both side we get e^{x}
– 2 = C tan y

Now putting y = π/4 and x = 0 we get C = -1

Required particular solution is

y = tan^{-1}(2 + e^{x} )

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

Question: 20: Solve the following differential equations

, given that x = 0 at y = 1

Solution Hint:

Simplify the differential equation we get

**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 }= r^{2}**x ^{2 }+ y^{2} = 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**

**(x ^{2 }+ y^{2})y' = 2y(x + yy’)**

**This is the required differential equation**

**Question 22**

**Find the differential equation of the family of curves y ^{2 }= 4ax**

**Ans: 2xyy' - y ^{2} = 0**

**Question 23**

**Find the solution of the differential equation **

**Solution Hint: Separate the variables and the integrating we get: **

**2e ^{2y} = x^{4} + C_{1}**

- Get link
- Other Apps

## Comments

## Post a Comment