This set of Mathematics Online Test for Class 12 focuses on “Differential Equations Basics-2 ”.

1. Find the order of the D.E \(\frac{2y”}{\sqrt{3}}-(2y’)^2+y=0\).

a) 4

b) 2

c) 1

d) 3

View Answer

Explanation: The highest order derivative in the given D.E is y”. Therefore, the order of the D.E is 2.

2. Find the order and degree of the D.E \(\left (\frac{d^3 y}{dx^3}\right )-3\left (\frac{d^2 y}{dx^2}\right )+2\left (\frac{dy}{dx}\right )^4+y^3=0\).

a) Order – 2, Degree – 4

b) Order – 2, Degree – 1

c) Order – 3, Degree – 1

d) Order – 1, Degree – 3

View Answer

Explanation: In the differential equation, the highest order derivative is \(\frac{d^3 y}{dx^3}\). Therefore, the order of the differential equation is 3. The given is a polynomial equation in \(\frac{d^3 y}{dx^3}\). Hence, the degree will be the power raised to \(\frac{d^3 y}{dx^3}\) i.e. 1

3. Find the degree of the differential equation \(\frac{d^3 y}{dx^3}+y^2\)=0

a) 5

b) 4

c) 2

d) 1

View Answer

Explanation: The given is a polynomial differential equation in \(\frac{d^3 y}{dx^3}\). Therefore, its degree will be the power raised to the highest order derivative \(\frac{d^3 y}{dx^3}\) which is 1.

4. Find the order of the differential equation –\(\left (\frac{3d^2 y}{dx^2}\right )+cos(y”)=0\)

a) 4

b) 1

c) 3

d) 2

View Answer

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

5. Find the degree of the differential equation \(3(\frac{d^2 y}{dx^2})-(\frac{dy}{dx})^2\)+siny=0.

a) 1

b) 3

c) 2

d) Not defined

View Answer

Explanation: In the polynomial differential equation \(3(\frac{d^2 y}{dx^2})-(\frac{dy}{dx})^2\)+siny=0, the power raised to the highest derivative \(\frac{d^2 y}{dx^2}\) is 1. Therefore, the degree of the differential equation is 1.

6. Find the order and degree of the differential equation 3y”-y’-e^{y}=0

a) Order – 2, Degree – Not defined

b) Order – 1, Degree – 1

c) Order – 1, Degree – Not defined

d) Order – 3, Degree – 3

View Answer

Explanation: In the differential equation 3y”-y’-e

^{y}=0, the highest order derivative is y”. Therefore, the order is 2. The D.E is not polynomial, so the degree of the differential equation is not defined.

7. The degree of the differential equation is not defined if it is not polynomial.

a) True

b) False

View Answer

Explanation: The given statement is true. The degree of a differential equation is defined only when the differential equation is a polynomial in its derivatives. The degree of a D.E will not be defined if it is not polynomial.

8. Find the degree of the D.E y’-10y=0.

a) 1

b) 2

c) 4

d) 3

View Answer

Explanation: The given differential equation is polynomial in y’. Therefore, the degree of the equation will be the power raised to the highest derivative y’ i.e. 1.

9. Find the order of the differential \(\left (\frac{d^2 y}{dx^3}\right )^3+5\) cosx-sinx=0

a) 3

b) 2

c) 1

d) 4

View Answer

Explanation: In the differential equation \(\left (\frac{d^2 y}{dx^3}\right )^3+5\) cosx-sinx=0, the highest order derivative is \(\frac{d^2 y}{dx^2}\). Therefore, the order of the differential equation is 2.

10. Find the degree of the equation \(8\left (\frac{d^2 y}{dx^2}\right )^2+2(\frac{dy}{dx})^2+y=0\).

a) 4

b) 1

c) 3

d) 2

View Answer

Explanation: The given differential equation is polynomial in \(\frac{d^2 y}{dx^2}\). Hence, the degree of the given D.E will be the power raised to the highest order derivative \(\frac{d^2 y}{dx^2}\) which is 2.

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