AP EAMCET · Maths · Differential Equations
The differential equation \(\frac{d y}{d x}=\frac{1}{a x+b y+c}\), where \(a, b, c\) are all non-zero real numbers, is
- A linear in y
- B linear in x
- C linear in both x and y
- D homogeneous equation
Answer & Solution
Correct Answer
(B) linear in x
Step-by-step Solution
Detailed explanation
Given differential equation, \(\begin{aligned} & \frac{d y}{d x}=\frac{1}{a x+b y+c} \\ & \frac{d y}{d x}=a x+b y+c \\ & \frac{d x}{d y}-a x=b y+c \end{aligned}\) Hence, this equation is a linear differential equation in \(x\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Two integers are drawn at random from the set \(\{5,6, . ., \ldots 35\}\). What is the probability that their difference is odd?AP EAMCET 2021 Medium
- If \(\left(x_1, y_1\right)\) and \(\left(x_2, y_2\right)\) are the end points of a focal chord of the parabola \(y^2=5 x\), then \(4 x_1 x_2+y_1 y_2\) is equal toAP EAMCET 2016 Easy
- The number of solutions of the equations \(x+y+z=1 ; x^2+y^2+z^2=1 ; x^3+y^3+z^3=1\) isAP EAMCET 2022 Medium
- The combined equation of the lines passing through the origin and having slopes \(\frac{2}{3}\) and \(\frac{-2}{3}\) isAP EAMCET 2020 Easy
- If origin is the ortho-center of an equilateral triangle whose vertices are \(\bar{a}, \bar{b}, \bar{c}\) thenAP EAMCET 2022 Easy
- \(\int_1^3 x^n \sqrt{x^2-1} d x=6\), then \(n=\)AP EAMCET 2022 Medium
More PYQs from AP EAMCET
- The number of subsets of \(\{1,2,3, \ldots, 9\}\) containing at least one odd number isAP EAMCET 2009 Medium
- The set of all points where the function f (x) = 2x| x|is differentiable isAP EAMCET 2021 Medium
- The equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve \(x^2+x y+y^2+x+3 y+1=0\) and the line \(x+y+2=0\) isAP EAMCET 2019 Hard
- Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all four cards of the same suit isAP EAMCET 2022 Easy
- In any
\[
\triangle A B C, \frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4 b^2 c^2}
\]
equals toAP EAMCET 2014 Hard - The maximun value of the applied force \(F\) such that the block as shown in the arrangement does not move is (Acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\) )
AP EAMCET 2019 Easy