TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\left(x^2+2\right)\) \(d y+2 x y d x=e^x\left(x^2+2\right) d x\) is
- A \(\frac{x}{y}=e^x\left(x^2+x-4\right)+c\)
- B \(2 x y=e^x\left(x^2-2 x+4\right)+c\)
- C \(\left(x^2+2\right) y=e^x\left(x^2-2 x+4\right)+c\)
- D \(\left(x^2+2\right)^2 y=e^x\left(x^2+2 x-4\right)+c\)
Answer & Solution
Correct Answer
(C) \(\left(x^2+2\right) y=e^x\left(x^2-2 x+4\right)+c\)
Step-by-step Solution
Detailed explanation
\(\left(x^2+2\right) d y+2 x y d x=e^x\left(x^2+2\right) d x\)…
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
- From a point \(P\) on the line \(4 x-3 y=6\) two tangents are drawn to the circle \(x^2+y^2-6 x-4 y+4=0\). If the angle between these tangents is \(\tan ^{-1}\left(\frac{24}{7}\right)\), then \(P=\)TS EAMCET 2018 Hard
- The number of solutions for \(z^3+\bar{z}=0\), isTS EAMCET 2014 Easy
- Let \(\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) and \(\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). If the orthogonal projection vector of \(\mathbf{a}\) on \(\mathbf{b}\) be \(\mathbf{x}\) and the orthogonal projection vector of \(\mathbf{b}\) on a be \(\mathbf{y}\), then \(|\mathbf{x}-\mathbf{y}|=\)TS EAMCET 2020 Easy
- The locus of all points that are at a distance greater than units from , isTS EAMCET 2019 Easy
- Let be any point on the circle and be its centre. Let be the chord of contact of with respect to the circle . Then the locus of the circumcentre of the triangle isTS EAMCET 2022 Medium
- If all the possible 3-digit numbers are formed using the digits \(1,3,5,7,9\) without repeating any digit, then the number of such 3 -digit numbers which are divisible by 3 isTS EAMCET 2024 Easy
More PYQs from TS EAMCET
- Let \(x+y=k\) be a normal to the parabola \(y^2=12 x\). If \(p\) is length of the perpendicular from the focus of the parabola onto this normal, then \(4 k-2 p^2\) is equal toTS EAMCET 2012 Medium
- Water is filled in a tank up to a height of 20 cm from the bottom of the tank. Water flows through a hole of area \(1 \mathrm{~mm}^2\) at its bottom. The mass of the water coming out from the hole in a time of 0.6 s is
(Density of water \(=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )TS EAMCET 2025 Medium - In the reaction, \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OC}_2 \mathrm{H}_5+\mathrm{CO} \underset{150^{\circ} \mathrm{C}, 500 \text { atm pressure }}{\stackrel{\mathrm{BF}_3}{\longrightarrow}} X\) What is \(X\) ?TS EAMCET 2003 Hard
- A line makes angles \(60^{\circ}, 45^{\circ}, \theta\) with positive \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively. If \(\theta\) is an acute angle, then \(\tan \theta=\)TS EAMCET 2025 Medium
- An AC generator \(10 \mathrm{~V}(\mathrm{rms})\) at \(200 \mathrm{rad} / \mathrm{s}\) is connected in series with a \(50 \Omega\) resistor, a \(400 \mathrm{mH}\) inductor and a \(200 \mu \mathrm{F}\) capacitor. The rms voltage across the inductor isTS EAMCET 2017 Easy
- The reduction potential of a half cell consisting of a Pt electrode immersed in \(2.0 \mathrm{M} \mathrm{Fe}^{2+}\) and \(0.02 \mathrm{M} \mathrm{Fe}^{3+}\) solution (in V) is Given \(\left(\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059, \mathrm{E}_{\mathrm{Fe}^{3+} \mid \mathrm{Fe}^{2+}}^0=0.771 \mathrm{~V}\right)\)TS EAMCET 2023 Medium