enEnglishguગુજરાતી
GUJCET · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}=e^{x-y}\) is ____________
- A \(e^x+e^y=c\)
- B \(e^{-x}+e^{-y}=c\)
- C \(e^{-x}+e^y=c\)
- D \(e^x-e^y=c\)
Answer & Solution
Correct Answer
(D) \(e^x-e^y=c\)
Step-by-step Solution
Detailed explanation
\(e^y dy = e^x dx\) \(\int e^y dy = \int e^x dx\)
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
- \(R =\left\{(\pi, \pi),\left(\pi^2, \pi^2\right),\left(\pi^3, \pi^3\right),\left(\pi,\pi^2\right),\left(\pi^2, \pi^3\right)\right\}\) is defined on set \(\left\{\pi, \pi^2, \pi^3\right\}\) then \(R\) is ____________ .GUJCET 2023 Easy
- The maximum value of \(Z=60 x+10 y\) whose, corner points are \((10,0),(2,4),(1,5)\) and \((0,8)\) is _________ .GUJCET 2019 Easy
- The particular solution of the differential equation \(\frac{d y}{d x}=-4 x y^2\) with initial condition \(x=0, y=1\) is ____________ .GUJCET 2023 Hard
- \(\sin ^{-1}\left(\sin \frac{23 \pi}{6}\right)=\) ____________ .GUJCET 2024 Hard
- If matrix \(A=\left[\begin{array}{ll}1 & 5 \\ 6 & 7\end{array}\right]\) and \(B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\) then, which of the following statement is incorrect?GUJCET 2021 Medium
- The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^{\frac{1}{2}}=\left(\frac{d^2 y}{d x^2}\right)^{1 / 3}\) is ___________ .GUJCET 2025 Medium
More PYQs from GUJCET
- If \(\left|\begin{array}{cc}\sin ^2 \theta & \cos ^2 \theta \\ -\cos ^2 \theta & \sin ^2 \theta\end{array}\right|=\) _________.GUJCET 2019 Hard
- What will be the name of product on ammonolysis of benzyl chloride and reaction of amine so formed with two moles of \(\mathrm{CH}_3 \mathrm{Cl} ?\)GUJCET 2026 Hard
- Benzene diazonium chloride reacts with phenol in basic medium to give product. How many \(\sigma\) (sigma) and \(\pi\) (pi) bonds are present in that product ?GUJCET 2023 Hard
- The formula for logistic growth curve is which?GUJCET 2021 Medium
- The charge density of uniformly charged infinite plane is \(\sigma\). A simple pendulum is suspended vertically downward near it. Charge \(q_0\) is placed on metallic bob. If the angle made by the string is \(\theta\) with vertical direction then _______.GUJCET 2020 Medium
- A parallel plate capacitor having air as dielectric medium is charged by a potential difference of V volt. After disconnecting the battery, the distance between the plates of the capacitor is increased using an insulated handle. As a result potential difference between the plates _________.GUJCET 2009 Medium