Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Differential Equations

NDA 2017 · Mathematics · Differential Equations

The differential equation of minimum order by eliminating the...

The differential equation of minimum order by eliminating the arbitrat constants A and C in the equatic y=A[sin⁡(x+C)+cos⁡(x+C)]\mathrm{y}=\mathrm{A}[\sin (\mathrm{x}+\mathrm{C})+\cos (\mathrm{x}+\mathrm{C})] is

Options

  1. Ay′′+(sin⁡x+cos⁡x)y′=1y^{\prime \prime}+(\sin x+\cos x) y^{\prime}=1
  2. By′′=(sin⁡x+cos⁡x)y′y^{\prime \prime}=(\sin x+\cos x) y^{\prime}
  3. Cy′′=(y′)2+sin⁡xcos⁡xy^{\prime \prime}=\left(y^{\prime}\right)^2+\sin x \cos x
  4. Dy′′+y=0y^{\prime \prime}+y=0

Correct answer

D. y′′+y=0y^{\prime \prime}+y=0

Step-by-step solution

y=A[sin⁡(x+c)+cos⁡(x+c)]\mathrmy′=A[cos⁡(x+c)−sin⁡(x+c)]\mathrmy′′=−A[sin⁡(x+c)+cos⁡(x+c)]=−y∴\mathrmy′′+y=0\begin{aligned} & \mathrm{y}=\mathrm{A}[\sin (\mathrm{x}+\mathrm{c})+\cos (\mathrm{x}+\mathrm{c})] \\ & \mathrmy^{\prime}=\mathrm{A}[\cos (\mathrm{x}+\mathrm{c})-\sin (\mathrm{x}+\mathrm{c})] \\ & \mathrmy^{\prime \prime}=-\mathrm{A}[\sin (\mathrm{x}+\mathrm{c})+\cos (\mathrm{x}+\mathrm{c})] \\ & =-\mathrm{y} \\ & \therefore \mathrmy^{\prime \prime}+\mathrm{y}=0\end{aligned}
Practice Differential Equations on Quantrex Academy →

More from Differential Equations

Passage: Consider the differential equation e^ x+y (dy)/(dx)=e^ x-y . Question: What is… NDA 2026What is the solution of the differential equation ((dy)/(dx))=p when y(0)=q ? NDA 2026Passage: Consider the differential equation e^ x+y (dy)/(dx)=e^ x-y . Question: What is… NDA 2026What is the degree of the differential equation ((d^2y)/(dx^2))^ (3)/(2) = ((dy)/(dx))^… NDA 2025If k is an arbitrary constant, then what is the general solution of the equation (x +… NDA 2025Consider the following statements:I. y = xe^ 2x is the solution of (dy)/(dx) = y (2 +… NDA 2025What are the order and degree respectively of the differential equation \ 2-((d y)/(d… NDA 2024Paragraph: Let y d x+(x-y^3) d y=0 be a differential equation. Question: What is the… NDA 2024The differential equation, representing the curve y=e^x(a x+b x) where a and b are… NDA 2024Paragraph: Let y d x+(x-y^3) d y=0 be a differential equation. Question: What are the… NDA 2024If (d y)/(d x)=2 e^x y^3, y(0)=(1)/(2) then what is 4 y^2 (2-e^x) equal to? NDA 2024Let y_1(x) and y_2(x) be two solutions of the differential equation (d y)/(d x)=x . If… NDA 2024A parabola pases through (1,2) and satisfies the differential equation (d y)/(d x)=(2… NDA 2023A parabola pases through (1,2) and satisfies the differential equation (d y)/(d x)=(2… NDA 2023What are the order and the degree respectively of the differential equation x^2((d^3… NDA 2023What is the differential equation of all parabolas of the type y^2=4 a(x-b) ? NDA 2023 Full Differential Equations list Differential Equations JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs