This set of Ordinary Differential Equations Multiple Choice Questions & Answers (MCQs) focuses on “First Order First Degree Differential Equations”.
1. What is the order of the differential equation given by \(\frac{dy}{dx} + 4y = sin x\)?
a) 0.5
b) 1
c) 2
d) 0
View Answer
Explanation: Since the order of a differential equation is defined as the order of the highest derivative occurring in the differential equation, i.e for nth derivative \(\frac{d^ny}{dx^n}\) if n=1.
It has order 1\(\rightarrow\) differential equation contains only \(\frac{dy}{dx}\) derivative with variables and constants.
2. Given the differential equation \(\frac{dy}{dx} = \frac{x^4-y^4}{(x^2+y^2)xy}\) the degree of differential equation is _____________
a) 1
b) 4
c) 0
d) 2
View Answer
Explanation: The degree of a differential equation is the degree of the highest order derivative when differential coefficients are free from radicals and fraction above differential i.e having first order is free from radical and a fraction has a power of 1 thus it has a degree of 1.
3. The process of formation of the differential equation is given in the wrong order, select the correct option from below given options.
1) Eliminate the arbitrary constants.
2) Differential equation which involves x,y,\(\frac{dy}{dx}.\)
3) Differentiating the given equation w.r.t x as many times as the number of arbitrary constants.
a) 1,2,3
b) 3,2,1
c) 3,1,2
d) 2,1,3
View Answer
Explanation: The correct order of forming differential equation is given by option 3,1,2, even the given differential equation can be solved by other order given in the option but the task becomes more tedious.
4. What is the degree of first order differential equation, given by \(\left(\frac{dy}{dx}\right)^{1.5} = \left(\frac{x cosx}{x^2+\sqrt{sinx}}\right)^3\)?
a) 1.5
b) 1
c) 3
d) 0.5
View Answer
Explanation: The degree of DE is obtained by removing all fraction and radicals from the power of the derivative occurring in the equation hence the equation becomes \( \frac{dy}{dx} = \left(\frac{x cosx}{x^2+\sqrt{sinx}}\right)^2\) which is first degree.
5. A racer accelerates from a stop so that its speed is 10t m/s t second after starting how far will the car go in 4 seconds?
a) 80m
b) 60m
c) 40m
d) 160m
View Answer
Explanation: Given \(\frac{dy(t)}{dt}=10t…\) where y(t) is the distance travelled a function of time above equation is a first order first degree DE where t varies from 0 to 4 seconds integrating on both side w.r.t t we get \(\int_0^4 dy(t) = \int_0^4 10t \,dt\) \(= y(4)-y(0) = \big[5t^2\big]_0^4….. \) but y(0) = 0 since car is at rest at time t=o
y(4) = 5(16) = 80m.
Sanfoundry Global Education & Learning Series – Ordinary Differential Equations.
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