KCET · Maths · Differential Equations
Solution of differential equating \(x d y-y d x=0\) represents
- A A rectangular hyperbola.
- B Parabola whose vertex is at origin.
- C Straight line passing through origin.
- D A circle whose centre is origin.
Answer & Solution
Correct Answer
(C) Straight line passing through origin.
Step-by-step Solution
Detailed explanation
Given, \(x d y=y d x\)
\(\Rightarrow \quad \frac{1}{y} d y=\frac{1}{x} d x\)
Integrating both sides,
\(\begin{aligned}
&\quad \int \frac{1}{y} d y=\int \frac{1}{x} d x \\
&\Rightarrow \quad \log y=\log x+\log c \\
&\Rightarrow y=x c \text { which is the equation of line passing } \\
&\text { through origin. }
\end{aligned}\)
\(\Rightarrow \quad \frac{1}{y} d y=\frac{1}{x} d x\)
Integrating both sides,
\(\begin{aligned}
&\quad \int \frac{1}{y} d y=\int \frac{1}{x} d x \\
&\Rightarrow \quad \log y=\log x+\log c \\
&\Rightarrow y=x c \text { which is the equation of line passing } \\
&\text { through origin. }
\end{aligned}\)
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
- The sum of the series, \(\frac{1}{2.3} \cdot 2+\frac{2}{3.4} \cdot 2^{2}+\frac{3}{4.5} \cdot 2^{3}+\ldots\) upto \(n\) terms isKCET 2013 Hard
- In the expansion of \((1+x)^n\)
\(\frac{C_1}{C_0}+2 \frac{C_2}{C_1}+3 \frac{C_3}{2}+\ldots+n \frac{C_n}{C_{n-1}}\) is equal toKCET 2024 Medium - The system of linear equations \( x+y+z=6, x+2 y+3 z=10 \) and \( x+2 y+a z=b \) has no
solutions whenKCET 2015 Easy - A box contains \( 6 \) red marbles numbers from \( 1 \) through \( 6 \) and \( 4 \) white marbles \( 12 \) through \( 15 . \)
Find the probability that a marble drawn 'at random' is white and odd numbered.KCET 2015 Easy - The domain of the function \(\sqrt{\dfrac{x-7}{9-x}}\) isKCET 2026 Easy
- A value of \(x\) satisfying \(150 x \equiv 35(\bmod 31)\) isKCET 2013 Easy
More PYQs from KCET
- The yellow precipitate formed during the chromyl chloride test is chemicallyKCET 2011 Medium
- Which one of the following statements is true?KCET 2010 Easy
- Which is the intermediate compound that links the end product of Glycolysis with TCA Cycle?KCET 2024 Easy
- Roquefort cheese is ripened byKCET 2023 Easy
- If \(|\mathbf{a}+\mathbf{b}|=|\mathbf{a}-\mathbf{b}|\), thenKCET 2023 Easy
- A copper rod \(A B\) of length \(l\) is rotated about end \(A\) with a constant angular velocity \(\omega\). The electric field at a distance \(x\) from the axis of rotation isKCET 2021 Hard