This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Differential Equations Basics-1”.

1. Find the order of the differential equation y’-20y+2=0.

a) 2

b) 8

c) 0

d) 1

View Answer

Explanation: In the given D. E the highest order derivative is y’. Therefore, the order of the given D.E is 1.

2. Find the order of the D.E \(\frac{7d^2 y}{dx^2}-\frac{6dy}{dx}\)=1

a) 4

b) 2

c) 3

d) 1

View Answer

Explanation: The highest order derivative in the given differential equation is \(\frac{d^2 y}{dx^2}\). Therefore, the order of the D.E is 2.

3. Find the order and degree of the differential equation y”’-(4y’)^{3}=0

a) Order -3, Degree-1

b) Order -1, Degree-3

c) Order -2, Degree-1

d) Order -3, Degree-2

View Answer

Explanation: In the D.E y”’-(4y’)

^{3}=0, the highest order derivative is y”’. Therefore, the order of the D.E is 3. Since it is a polynomial equation, the degree will be the power raised to y”’. Therefore, the degree is 1.

4. Find the order of the differential equation \(\frac{dy}{dx}\)+15 cosx=0.

a) 4

b) 3

c) 2

d) 1

View Answer

Explanation: The highest order derivative in the given D.E is \(\frac{dy}{dx}\). Hence, the order of the given differential equation is 1.

5. Find the degree of the differential equation y”-12cosec y=0.

a) 1

b) 2

c) 4

d) Not defined

View Answer

Explanation: The highest order derivative in this D.E is y”. The given D.E is a polynomial equation in y”. Therefore, the degree of the D.E is the power raised to y” which is 1.

6. Find the order and degree of the differential equation 7y’-3y=0.

a) Order -1, Degree-2

b) Order -2, Degree-3

c) Order -1, Degree-1

d) Order -3, Degree-2

View Answer

Explanation: In the given D.E, the highest order derivative is y’. Therefore, the order is 1. The given D.E 7y’-3y=0 is a polynomial equation in y’ and the power raised to the highest derivative is 1. Hence, the degree is 1.

7. Find the degree of the D.E \(\frac{d^2 y}{dx^2}+5 cot(\frac{dy}{dx})\)=0

a) five

b) three

c) two

d) not defined

View Answer

Explanation: The given differential equation is not polynomial. Hence, the degree of the differential equation will not be defined.

8. Find the order and degree of the differential equation (y”’)^{2}+7(y’)^{2}-(cosx)^{2}=0

a) Order- 0, Degree-2

b) Order- 3, Degree-2

c) Order- 3, Degree-3

d) Order- 1, Degree-2

View Answer

Explanation: The highest order derivative in the equation is y”’. Hence, the order is 3. The equation is polynomial in y”’. Therefore, the degree of the D.E will be the power of the derivative y”’ i.e. 2.

9. Find the degree of the D.E (\(\frac{d^2 y}{dx^2}\))-3 tanx=0.

a) 2

b) 1

c) 3

d) 4

View Answer

Explanation: The given equation is a polynomial differential equation. Therefore, the degree of the equation will the power of the highest derivative \(\frac{d^2 y}{dx^2}\) i.e. 1.

10. Find the order of the differential equation \(\frac{9d^2 y}{dx^2}-\frac{7dy}{dx}+y^6=0\)

a) 3

b) 1

c) 4

d) 2

View Answer

Explanation: The highest derivative of the given D.E is \(\frac{d^2 y}{dx^2}\). Therefore, the order is 2.

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