MHT CET · Maths · Differential Equations
The particular solution of the differential equation \(x d y+2 y d x=0\), when \(x=2\)
and \(y=1\) is
- A \(x y^{2}=4\)
- B \(x^{2} y=4\)
- C \(x^{2} y=-4\)
- D \(x y^{2}=-4\)
Answer & Solution
Correct Answer
(B) \(x^{2} y=4\)
Step-by-step Solution
Detailed explanation
Given D.E. is \(x d y+2 y d x=0\)
\(\therefore x d y=-2 y d x \Rightarrow \int \frac{d y}{y}=\int-\frac{2 d x}{x}\)
\(\log y=-2 \log x+\log c \Rightarrow \log y+2 \log x=\log c\)
\(\therefore \quad \log y+\log x^{2}=\log c \Rightarrow x^{2} y=c\)
when \(x=2, y=1, c=4\)
\(\therefore\) Particular solution is \(\mathrm{x}^{2} \mathrm{y}=4\)
\(\therefore x d y=-2 y d x \Rightarrow \int \frac{d y}{y}=\int-\frac{2 d x}{x}\)
\(\log y=-2 \log x+\log c \Rightarrow \log y+2 \log x=\log c\)
\(\therefore \quad \log y+\log x^{2}=\log c \Rightarrow x^{2} y=c\)
when \(x=2, y=1, c=4\)
\(\therefore\) Particular solution is \(\mathrm{x}^{2} \mathrm{y}=4\)
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 cofactors of the elements of second row of the matrix \(\left[\begin{array}{ccc}1 & 3 & 2 \\ -2 & 0 & 1 \\ 5 & 2 &1\end{array}\right]\) isMHT CET 2020 Easy
- The angle between the line \(x=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}-3}{\lambda}\) and the plane \(x+2 y+3 z=6\) is \(\cos ^{-1} \sqrt{\frac{5}{14}}\), then the value of \(\lambda\) isMHT CET 2025 Medium
- The value of \(\int \frac{x+1}{x\left(1+x e^x\right)^2} \mathrm{~d} x\) is equal toMHT CET 2024 Medium
- \(\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}\) are three vectors such that \(\vec{a}=x \vec{b}+y \vec{c}\), then \(x+y=\)MHT CET 2021 Medium
- \(\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x=\)MHT CET 2020 Easy
- If the points \(\mathrm{A}(1,1,2), \mathrm{B}(2,1, \mathrm{p}), \mathrm{C}(1,0,3)\) and \(\mathrm{D}(2,2,0)\) are coplanar then the value of \(p\) isMHT CET 2025 Medium
More PYQs from MHT CET
- Which hormone in barley and wheat seeds promotes germination by synthesizing amylase enzyme?MHT CET 2022 Medium
- What is the number of amino acids present in single turn of \(\alpha\)-helix of protein?MHT CET 2024 Easy
- A transverse wave travelling along a stretched string has a speed of \(30 \mathrm{~m} / \mathrm{s}\) and a frequency of 250 Hz. The phase difference between two points on the string 10 cm apart at the same instant isMHT CET 2024 Medium
- A train has to negotiate a curve of radius 'r' \(\mathrm{m}\), the distance between the rails is \({ }^{\prime}{ }^{\prime} \mathrm{m}\) and outer rail is raised above inner rail by distance of ' \(\mathrm{h}^{\prime} \mathrm{m}\). If the angle of banking is small, the safety speed limit on this banked road isMHT CET 2020 Easy
- Consider \(\overrightarrow{\mathrm{r}}, \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{c}}\) are non-zero vectors such that \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{a}}=0\), \(|\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{r}}||\overrightarrow{\mathrm{b}}|,|\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{c}}|=|\overrightarrow{\mathrm{r}}||\overrightarrow{\mathrm{c}}|\), then \([\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}]\) isMHT CET 2023 Medium
- Which one of the following cross will have 1:1:1:1 ratio of progeny?MHT CET 2019 Medium