AP EAMCET · Maths · Differential Equations
Solve the differential equation : \(\frac{d y}{d x}=e^{x+y}\)
- 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
(C) \(e^x+e^{-y}=c\)
Step-by-step Solution
Detailed explanation
\[ \text { } \begin{aligned} \frac{d y}{d x} & =e^{x+y} \\ \frac{d y}{d x} & =e^x \cdot e^y \Rightarrow \frac{d y}{e^y}=e^x d x \\ e^{-y} d y & =e^x d x \end{aligned} \] Integrating both sides,…
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
- \(L_1\) and \(L_2\) are two lines having slopes 2 and \(-\frac{1}{2}\) respectively. If both \(L_1\) and \(L_2\) are concurrent with the lines \(x-y+2=0\) and \(2 x+y+3=0\), then sum of the absolute values of the intercepts made by the lines \(L_1\) and \(L_2\) on the coordinate axes isAP EAMCET 2025 Medium
- If \(\frac{x^2}{a}+\frac{2 x y}{h}+\frac{y^2}{b}=0\) represents a pair of straight lines such that the slope of one of the lines is twice the other, then \(\frac{a b}{h^2}=\)AP EAMCET 2017 Medium
- If the number of elements in the sets \(G\) and \(A\) are 3 and 4 respectively, then match the items of List I with those of List II
The correct match is
A B C DAP EAMCET 2019 Medium - If the angle between the asymptotes of a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \(2 \operatorname{Tan}^{-1}\left(\frac{2}{3}\right)\) and \(\mathrm{a}^2-\mathrm{b}^2=45\), then \(\mathrm{ab}=\)AP EAMCET 2025 Medium
- If the angle between the asymptotes of the hyperbola \(x^2-k y^2=3\) is \(\frac{\pi}{3}\) and \(e\) is its eccentricity, then the pole of the line \(x+y-1=0\) with respect to this hyperbola isAP EAMCET 2024 Medium
- If a parabola passess through the points \((-2,1)\), \((1,2)\) and \((-1,3)\) having horizontal axis, then the length of the latus rectum of that parabola isAP EAMCET 2018 Medium
More PYQs from AP EAMCET
- The least value of \(n\) such that \({ }^{(n-1)} C_6+{ }^{(n-1)} C_7 < { }^n C_8\) isAP EAMCET 2023 Easy
- If \(z \in C\) and \(i z^3+4 z^2-z+4 i=0\), then a complex root of this equation having minimum magnitude isAP EAMCET 2018 Hard
- If a circle is inscribed in an equilateral triangle of side a, then the area of any square (in sq. units) inscribed in this circle isAP EAMCET 2024 Medium
- Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipeAP EAMCET 2020 Easy
- Let \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=-5 \hat{i}+7 \hat{j} \quad\) and \(\quad \vec{c}=3 \hat{i}+y \hat{j} \quad\) be three vectors such that \(|\vec{a}-\vec{b}+\vec{c}|=\sqrt{141}\). If \(y_1\) and \(y_2\) are the values of \(y\) satisfying the given condition, then \(\left|\mathrm{y}_1-\mathrm{y}_2\right|=\)AP EAMCET 2023 Easy
- A source of sound of frequency \(640 \mathrm{~Hz}\) is moving at a velocity of \(\frac{100}{3} \mathrm{~m} / \mathrm{s}\) along a road, and is at an instant \(30 \mathrm{~m}\) away from a point \(A\) on the road (as shown in figure). A person standing at \(O, 40 \mathrm{~m}\) away from the road hears sound of apparent frequency \(v^{\prime}\). The value of \(v^{\prime}\) is (velocity of sound \(=340 \mathrm{~m} / \mathrm{s}\) )
AP EAMCET 2013 Hard