MTH401 Midterm Quiz solution by taleemi markaz part 1

MTH401 GRAND QUIZ 100% correct Solution 2024
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Questions:
The differential equation
𝒅𝒖/𝒅𝒙+𝟐/𝒙 𝒅𝒙=𝟑−𝟔/𝒙
has an integrating factor
General solution of the separable differential equation
(〖𝒔𝒆𝒄〗^𝟐 𝒚)/𝒕𝒂𝒏⁡𝒚 𝒅𝒚=𝒅𝒙
is ……..
General solution of the separable differential equation
𝒅𝒚/(𝟏+𝒚^𝟐 )=𝟐𝒙𝒅𝒙
is ……..
Which of following is an example of Homogeneous function?
Which of following is the Homogeneous function?
(𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )+𝟓(𝒅𝒚/𝒅𝒙)^𝟑−𝟑𝐲=𝒆^𝒔𝒊𝒏⁡𝒙 is an example of ______ differential equation.
𝒚𝒅𝒙−𝒚(𝒔𝒊𝒏𝒙)𝒅𝒚=𝟎 is an example of ______ differential equation.
Classify the following differential equation
𝒆^𝒙 𝒅𝒚/𝒅𝒙+𝟐𝒚=𝟑𝒙𝒚
The order of the differential equation (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )+𝟓(𝒅𝒚/𝒅𝒙)^𝟑−𝟑𝒚=𝒆^𝐬𝐢𝐧⁡𝒙 is ………..
Which of the following function would satisfy 𝒅𝒚/𝒅𝒙=(𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )=…=(𝒅^𝒏 𝒚)/(𝒅𝒙^𝒏 )?
Which of the following is a constant solution of separable differential equation
𝒅𝒚/𝒅𝒙=(𝒙+√𝒙)(𝒚+√𝒚)
In exponential model for the population growth
For 𝒇(𝒙,𝒚)=𝟐𝒙/𝟑𝒚+𝟕, 𝒇(𝒕𝒙,𝒕𝒚)= _________
If we substitute 𝒖=𝒚/𝒙 in differential equation
𝒙 𝒅𝒚/𝒅𝒙−𝒚=𝒙^𝟑/𝒚 𝒆^(𝒚⁄𝒙)
Then the given differential equation can be simplified to
If 𝒅(𝒙^𝟐/𝒚)=𝟎 is an equivalent form of the exact differential equation −𝒙^𝟐 𝒅𝒚=𝟎 , then its solution is ______
The differential equation (𝒙+𝟐𝒚^𝟑 ) 𝒅𝒚/𝒅𝒙=𝒚 is linear in unknown _____
The differential equation of orthogonal trajectory to the family of curves 𝒙^𝟐+𝒚^𝟐=𝒄^𝟐 is
The differential equation of orthogonal trajectory to the family of curves 𝒙−𝟐𝒚=𝒄 is
For 2nd order linear non-homogeneous differential equation
𝒂_𝟐 (𝒙) (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )+𝒂_𝟏 (𝒙) 𝒅𝒚/𝒅𝒙+𝒂_𝟎 (𝒙)𝒚=𝒈(𝒙)
,which of the following is NOT the pair of boundary condition ______________