Mathematics Questions and Answers – Differential Equations Basics-2

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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

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

Answer: c
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

Answer: d
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.
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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

Answer: d
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 \(3(\frac{d^2 y}{dx^2})-(\frac{dy}{dx})^2\)+sin⁡y=0.
a) 1
b) 3
c) 2
d) Not defined
View Answer

Answer: a
Explanation: In the polynomial differential equation \(3(\frac{d^2 y}{dx^2})-(\frac{dy}{dx})^2\)+sin⁡y=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.
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6. Find the order and degree of the differential equation 3y”-y’-ey=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

Answer: a
Explanation: In the differential equation 3y”-y’-ey=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

Answer: a
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.
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8. Find the degree of the D.E y’-10y=0.
a) 1
b) 2
c) 4
d) 3
View Answer

Answer: a
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 \(\left (\frac{d^2 y}{dx^3}\right )^3+5\) cos⁡x-sin⁡x=0
a) 3
b) 2
c) 1
d) 4
View Answer

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

Answer: d
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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter