CUET · MATHS · PYQ PAPER 2023
The general solution of the differential equation \(\frac{d y}{d x}=1+x+y+x y\) is given by:
- A \(\log (1+y)=x+\frac{x^2}{2}+C\), where \(C\) is a constant
- B \(\log y=x+\frac{x^2}{2}+C\), where \(C\) is a constant
- C \(\log (y-1)=x+\frac{x^2}{2}+C\), where \(C\) is a constant
- D \(\log (1+y)=x-\frac{x^2}{2}+C\), where \(C\) is a constant
Answer & Solution
Correct Answer
(D) \(\log (1+y)=x-\frac{x^2}{2}+C\), where \(C\) is a constant
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=(1+x)(1+y)\) \(\int \frac{d y}{1+y}=\int (1+x) d x\) \(\log (1+y)=x+\frac{x^2}{2}+C\)
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 normal distribution curve is symmetrical about[ \(\mu=\) mean, \(\sigma=\) standard deviation]CUET 2025 Medium
- For a set A = {1, 2, 3}, the following functions are defined from A to A. Which of these functions has an inverse?CUET 2023 Medium
- The slope of the normal to the curve \(y=x^3-4 \sin x\) at \(x=0\) is:CUET 2023 Easy
- If \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=5,|\vec{b}|=3,|\vec{c}|=7\), then the acute angle between \(\vec{a}\) and \(\vec{b}\) isCUET 2025 Medium
- If \(A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], \quad B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]\) and \(A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]\), then the value of \((x, y)\) is:CUET 2023 Medium
- A player participates in 3 matches against three teams \(T_1, T_2\) and \(T_3\). The probability of winning a match against teams \(T_1, T_2\) and \(T_3\) are \(0.2,0.3\) and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he
(A) wins all the 3 matches is 0.054
(B) wins no match is 0.054
(C) wins exactly two matches is 0.348
(D) wins exactly one match is 0.542
Choose the correct answer from the options given below :CUET 2025 Hard
More PYQs from CUET
- Identify the correct sequence of events during menstrual cycle?
(A) Next cycle begins
(B) Proliferative phase
(C) Menstruation
(D) Secretory phase
Choose the correct answer from the options given below:CUET 2025 Medium - Anisole on heating with concentrated HI gives:CUET 2025 Medium
- If \(A\) is a non-singular matrix of order 3 such that \(|\operatorname{adj}(A)|=121\), then \(\left|A A^T\right|\) is equal to :CUET 2025 Medium
- Let \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}4 & -6 \\ -2 & 4\end{array}\right]\), then
(A) \(\operatorname{det}\left(A^T\right)=1\)
(B) \(A B=I\), where \(I\) is the identity matrix of order 2
(C) \(A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]\)
(D) \(\operatorname{adj}(B)=\left[\begin{array}{ll}4 & 2 \\ 6 & 4\end{array}\right]\)
Choose the correct answer from the options given below :CUET 2025 Hard - Which one of the following equation represent Verhulst Pearl Logistic Growth?CUET 2025 Medium
- The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{\frac{2}{3}}=4 \frac{d^3 y}{d x^3}\) respectively are:CUET 2023 Easy