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Published on: 29/08/2019
Differential Equations
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Questions + Answers key
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1.
Write the degree of the differential equation :
\(\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }-2\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -\frac { dy }{ dx } +1=0\)
2.
Write the degree of the differential equation : \({ x }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 3 }+y\left( \frac { dy }{ dx } \right) ^{ 4 }+{ x }^{ 3 }=0\)
3.
Write the degree of the differential equation \({ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+x\left( \frac { dy }{ dx } \right) ^{ 4 }=0\)
4.
Write the degree of the differential equation \(\left( \frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \right) ^{ 2 }+\left( \frac { ds }{ dt } \right) ^{ 3 }+4=0\)
5.
Write the order and degree of the differential equation \(x-cos(\frac{dy}{dx})=0.\)
6.
Write the order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{3}-5 \frac{d y}{d x}+6=0\)
7.
Write the degree of the differential equation:\({ \left( \frac { dy }{ dx } \right) }^{ 4 }+3x\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0\)
8.
Write the degree of the differential equation: \(x{ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+y{ \left( \frac { dy }{ dx } \right) }^{ 2 }+{ x }^{ 3 }=0.\)
9.
Write the degree of the differential equation: \(5x{ \left( \frac { dy }{ dx } \right) }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0.\)
10.
What is the degree of the following differential equation?
\({ { 5x\left( \frac { dy }{ dx } \right) } }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -6y=logx\)
1.
The highest order derivative is \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) and its highest power is 2.
So, the degree of differential equation is 2.
2.
The highest order derivative is \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) and its power is 3.
So, the degree of differential equation is 3.
3.
Given \({ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+x\left( \frac { dy }{ dx } \right) ^{ 4 }=0\)
The highest order derivative is \(\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) \) and its power is 2.
So, the degree of differential equation is 2.
4.
\(\left( \frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \right) ^{ 2 }+\left( \frac { ds }{ dt } \right) ^{ 3 }+4=0\)
In the given differential equation, the power of highest order derivative i.e., \(\frac { { d }^{ 2 }s }{ { dt }^{ 2 } } =2\)
\(\therefore \) Its degree = 2
5.
Highest order derivative in the equation is \(\frac {dy}{dx}\). Hence, order of the differential equation is 1.
Also \(x-\cos \left(\frac{d y}{d x}\right)=0 \Rightarrow \cos \left(\frac{d y}{d x}\right)=x \Rightarrow \frac{d y}{d x}=\cos ^{-1} x\)
Differntial equation can be written can be written as polynomial of derivates. Hence, degree is 1.
6.
Order =2; degree = 3.
7.
Degree = 1
8.
Degree = 3
9.
Degree = 1
10.
Degree of differential equation
\(-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } { { +5x\left( \frac { dy }{ dx } \right) } }^{ 2 }-6y\) = logx, is 1
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