Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differential Equations

NDA 2023 · Mathematics · Differential Equations

A solution of the differential equation ((d y)/(d x))^2-x (d y)/(d...

A solution of the differential equation \left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0$ is

Options

  1. Ay=2xy=2 x
  2. By=2x+4y=2 x+4
  3. Cy=x2−1y=x^2-1
  4. Dy=\frac{\left(x^2-2\right)}{2}

Correct answer

D. y=\frac{\left(x^2-2\right)}{2}

Step-by-step solution

(dydx)2−x(dydx)=0dydx[dydx−]=dydx=0\left(\frac{d y}{d x}\right)^2-x\left(\frac{d y}{d x}\right)=0\frac{d y}{d x}\left[\frac{d y}{d x}-\right]=\frac{d y}{d x}=0 or dydx=x\frac{d y}{d x}=x New dy=xdx⇒∫dy=∫xdxy=x22+C⇒y=x2+2C2y=x22+C⇒y=x2+2C2d y=x d x\Rightarrow \int d y=\int x d xy=\frac{x^2}{2}+C \Rightarrow y=\frac{x^2+2 C}{2}y=\frac{x^2}{2}+C \Rightarrow y=\frac{x^2+2 C}{2} Comparing with options, y=x2−22y=\frac{x^2-2}{2}
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