Differential Equation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

The order & degree of the differential equation `[1+(\frac{dy}{dx})^2]^{5/2}=\frac{d^3y}{dx^3}` is -- (i) 2,3 (ii) 3,2 (iii) 3,5 (iv) 5,2
Ans: (ii) 3,2
SEE SOLUTION

Question No: #2

The order & degree of the differential equation `(\frac{d^3y}{dx^3})^{2/3}=a[1+(\frac{dy}{dx})^6]^{3/2}` is -- (i) 3,4 (ii) 3,6 (iii) 3,2 (iv) 4,3
Ans: (i) 3,4
SEE SOLUTION

Question No: #3

The order and degree of differential equation `\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{1/3}+x^{1/4}=0` is -- (i) 2,3 (ii) 2,12 (iii) 2,6 (iv) 2,4
Ans: (i) 2,3
SEE SOLUTION

Question No: #4

Find order and degree of differential equation `2\frac{d^2y}{dx^2}+3\sqrt{1-(\frac{dy}{dx})^3}-y=0`
Ans: Order = 2, degree = 2
SEE SOLUTION

Question No: #5

The order of the differential equation `(\frac{d^4y}{dx^4})^3-\frac{d^3y}{dx^3}=\sqrt{1+\frac{dy}{dx}}` is -- (i) 3 (ii) 4 (iii) 6 (iv) 7
Ans: (ii) 4
SEE SOLUTION

Question No: #6

The order and degree of differential equation `\sqrt{y+\frac{d^2y}{dx^2}}=x+(\frac{dy}{dx})^{3/2}` is -- (i) 2, 2 (ii) 2, 3 (iii) 2, 4 (iv) 2, 1
Ans: (i) 2, 2
SEE SOLUTION

Question No: #7

Order of differential equation `(\frac{d^py}{dx^p})^2+(\frac{d^qy}{dx^q})^s+y^{1/r}=0` (where `p\gtq\gtr\gts`) is -- (i) 2 (ii) `s` (iii) `2r` (iv) `p`
Ans: (iv) `p`
SEE SOLUTION

Question No: #8

Find order & degree of differential equation `(\frac{d^py}{dx^p})^2-(\frac{d^qy}{dx^q})^{1/r}+(\frac{d^sy}{dx^s})^t=0` where `p\gt\q\gtr\gts\gtt`
Ans: Order = `p`, degree = `2r`
SEE SOLUTION

Question No: #9

Find order & degree of differential equation `\frac{d^4y}{dx^4}+\sin(\frac{d^3y}{dx^3})=0`
Ans: Order =4, degree = undefined
SEE SOLUTION

Question No: #10

Find order & degree of differential equation `\frac{d^3y}{dx^3}+x(\frac{dy}{dx})^4=4\ln(\frac{d^4y}{dx^4})`.
Ans: Order =4, degree = undefined
SEE SOLUTION