Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
MCQ
The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}\text{is}$
  • ✓
    $\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
  • B
    $\text{e}^{\text{x}}+\text{e}^{\text{y}}=\text{C}$
  • C
    $\text{e}^{-\text{x}}+\text{e}^{\text{y}}=\text{C}$
  • D
    $\text{e}^{-\text{x}}+\text{e}^{-\text{y}}=\text{C}$
✓

Answer

Correct option: A.
$\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
The given differential equation is

$\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x+y}}\ \ \text{or}\ \ \frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}}.\text{e}^{\text{y}}$

Separating the variables, we get,

$\frac{1}{\text{e}^{\text{y}}}\text{dy}=\text{e}^\text{x}\ \text{dx}$

$\text{Integrating},\ \int\text{e}^{-\text{y}}\text{dy}=\int\text{e}^\text{x}\ \text{dx}$

$\therefore\ \frac{\text{e}^{-\text{y}}}{-1}=\text{e}^\text{x}+\text{c}'$

$\therefore\ -\text{e}^{-\text{y}}=\text{e}^\text{x}+\text{c}'\ \ \text{or}\ \ \text{e}^\text{x}+\text{e}^{-\text{y}}=-\text{c}'$

$\therefore\ \text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C},$ which is required solution.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

On the power set P of a non-empty set A, we define an operation $\triangle \text{ by }\text{X}\triangle\text{Y}=(\text{X}\cap\text{Y})∪(\text{X}∩\text{Y})\text{X}\triangle\text{Y}=\text{X}∩\text{Y}∪\text{X}∩\text{Y}$
Then which are of the following statements is true about $\triangle$
→
Choose the correct answer from the given four options. The feasible solution for a $\text{LPP}$ is shown in. Let $Z = 3x - 4y$ be the objective function.

Minimum of $Z$ occurs at :
→
The value of $\big[\vec{\text{a}}-\vec{\text{b}},\vec{\text{b}}-\vec{\text{c}},\vec{\text{c}}-\vec{\text{a}}\big],$ where $\big|\vec{\text{a}}\big|=1,\big|\vec{\text{b}}\big|=5,\big|\vec{\text{c}}\big|=3,$ is:
→
The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:
→
$\int_{}^{} {\frac{{dx}}{{x[{{(\log x)}^2} + 4\log x - 1]}}} = $
→
If two sides of a triangle be given, then the area of the triangle will be maximum if the angle between the given sides be
→
Choose the correct answer from the given four options.
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is:
→
Choose the correct answer from the given four option.The integrating factor of the differential equation $\frac{\text{d}\text{y}}{\text{d}\text{x}}+\text{y}=\frac{1+\text{y}}{\text{x}}$ is:
→
Differential coefficient of $\sqrt {\sec \sqrt x } $ is
→
For every point $P(x, y, z)$ on the $x-$ axis $($except the origin$),$
→