Which of the following differential equations given below has the solution y=log⁡x?(a) \(\frac{d^2 y}{dx^2}\)-x=0(b) \(\frac{d^2 y}{dx^2}+(\frac{dy}{dx})^2\)=0(c) \(\frac{d^2 y}{dx^2}\)–\(\frac{dy}{dx}\)=0(d) x \(\frac{d^2 y}{dx^2}\)-log⁡x=0The question was asked during an internship interview.This is a very interesting question from General and Particular Solutions of Differential Equation in division Differential Equations of Mathematics – Class 12

Which of the following differential equations given below has the solu

1.	Which of the following differential equations given below has the solution y=log⁡x?(a) \(\frac{d^2 y}{dx^2}\)-x=0(b) \(\frac{d^2 y}{dx^2}+(\frac{dy}{dx})^2\)=0(c) \(\frac{d^2 y}{dx^2}\)–\(\frac{dy}{dx}\)=0(d) x \(\frac{d^2 y}{dx^2}\)-log⁡x=0The question was asked during an internship interview.This is a very interesting question from General and Particular Solutions of Differential Equation in division Differential Equations of Mathematics – Class 12
Answer» Right CHOICE is (B) \(\frac{d^2 y}{dx^2}+(\frac{dy}{dx})^2\)=0 The best I can explain: Consider the function y=log⁡X DIFFERENTIATING w.r.t x, we get \(\frac{dy}{dx}=\frac{1}{x} \)–(1) Differentiating (1) w.r.t x, we get \(\frac{d^2 y}{dx^2}=-\frac{1}{x^2} \) ∴\(\frac{d^2 y}{dx^2}+(\frac{dy}{dx})^2=-\frac{1}{x^2}+(\frac{1}{x})^2\) =-\(\frac{1}{x^2}+\frac{1}{x^2}\)=0.

Discussion

No Comment Found

Related InterviewSolutions

If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x?(a) x^2 d^2 y/dx^2 – xdy/dx + y = 0(b) x^2 d^2 y/dx^2 + xdy/dx + y = 0(c) x^2 d^2 y/dx^2 + xdy/dx – y = 0(d) x^2 d^2 y/dx^2 – xdy/dx – y = 0I have been asked this question in quiz.My doubt is from Linear Second Order Differential Equations topic in section Differential Equations of Mathematics – Class 12
Which of the following is the valid differential equation x = a cos(αt + β)?(a) d^2x/dt^2 – αx = 0(b) d^2x/dt^2 + αx = 0(c) d^2x/dt^2 – α^2x = 0(d) d^2x/dt^2 + α^2x = 0This question was addressed to me in a national level competition.This intriguing question originated from Linear Second Order Differential Equations topic in chapter Differential Equations of Mathematics – Class 12
The function y=3 cos⁡x is a solution of the function \(\frac{d^2 y}{dx^2}-3\frac{dy}{dx}\)=0.(a) True(b) FalseThis question was posed to me during an internship interview.Enquiry is from General and Particular Solutions of Differential Equation topic in chapter Differential Equations of Mathematics – Class 12
Which of the following functions is a solution for the differential equation y”+6y=0?(a) y=5 cos⁡3x(b) y=5 tan⁡3x(c) y=cos⁡3x(d) y=6 cos⁡3xThis question was posed to me in an online quiz.I need to ask this question from General and Particular Solutions of Differential Equation topic in section Differential Equations of Mathematics – Class 12
Which of the following functions is a solution for the differential equation xy’-y=0?(a) y=4x(b) y=x^2(c) y=-4x(d) y=2xThe question was posed to me in homework.My question is taken from General and Particular Solutions of Differential Equation topic in section Differential Equations of Mathematics – Class 12
Which of the following functions is the solution of the differential equation \(\frac{dy}{dx}\)+2y=0?(a) y=-2e^-x(b) y=2e^x(c) y=e^-2x(d) y=e^2xI got this question during an internship interview.The above asked question is from General and Particular Solutions of Differential Equation topic in division Differential Equations of Mathematics – Class 12
Find the degree of the differential equation \(\frac{d^3 y}{dx^3}+y^2\)=0(a) 5(b) 4(c) 2(d) 1The question was posed to me during an interview for a job.The question is from Differential Equations Basics-2 in chapter Differential Equations of Mathematics – Class 12
What is the solution of the given equation (D + 1)^2y = 0 given y = 2 loge 2 when x = loge 2 and y = (4/3) loge3 when x = loge3?(a) y = 4xe^-x(b) y = 4xe^x(c) y = -4xe^-x(d) y = -4xe^xThis question was addressed to me in a national level competition.I'd like to ask this question from Linear Second Order Differential Equations in section Differential Equations of Mathematics – Class 12
Which one of the following is correct if we differentiate the equation xy = ae^x + be^-x two times?(a) x(d^2y/ dx) + 2(dy/dx) = xy(b) x(d^2y/ dx) – 2(dy/dx) = xy(c) 3x(d^2y/ dx) + 2(dy/dx) = xy(d) x(d^2y/ dx) + 2(dy/dx) = 2xyThis question was posed to me in an interview for internship.I need to ask this question from Linear Second Order Differential Equations in chapter Differential Equations of Mathematics – Class 12
Find the particular solution for the differential equation \(\frac{dy}{dx}=\frac{3x^2}{7y}\) given that, y=1 when x=1.(a) 7x^2=2y^3+5(b) 7x^3=2y^2+5(c) 7y^2=2x^3+5(d) 2y^2=5x^3+6I got this question during an online interview.This interesting question is from Methods of Solving First Order & First Degree Differential Equations topic in portion Differential Equations of Mathematics – Class 12

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment