Download App

DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS1 Mark
Question
The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}\text{is}$
  1. $\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
  2. $\text{e}^{\text{x}}+\text{e}^{\text{y}}=\text{C}$
  3. $\text{e}^{-\text{x}}+\text{e}^{\text{y}}=\text{C}$
  4. $\text{e}^{-\text{x}}+\text{e}^{-\text{y}}=\text{C}$
✓

Answer

  1. $\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:
  1. a = 2b
  2. 2a = b
  3. a = b
  4. 3a = b
→
If $f :A \rightarrow B$ given by $3^{f(x)} + 2^{-x} = 4$ is a bijection, then
→
If A and B are two events such that P(A) = 0.4, P(B) = 0.3 and $\text{P}(\text{A}\cup\text{B})=0.5,$ then $\text{P}(\overline{\text{B}}\cap\text{A})$ equals.
→
If $A=\left[3 1 7 5\right]$ and $A ^2+ xI = yA$ then the values of $x$ and $y$ are
→
The maximum value of $\text{f}(\text{x})=\frac{\text{x}}{4-\text{x}+\text{x}^{2}}$ on $[-1, 1]$ is:
→
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
  4. None of these.
→
If $\text{A}=\begin{bmatrix}a^2 &\text{amp; ab}&\text{amp; ac} \\\text{ab}&\text{amp; }\text{b}^2&\text{amp;}\text{ bc}\\\text{ac}&\text{amp;}\text{bc}&\text{amp;}\text{c}^2 \end{bmatrix}$and $\text{a}^2+\text{b}^2+\text{c}^3=1$ then $\text{A}^2=$
  1. $2\text{A}$
  2. $\text{A}$
  3. $3\text{A}$
  4. $\frac{1}{2}\text{A}$
→
Which of the following represents coinitial vector:
  1. c, d
  2. m, b
  3. b, d
  4. Both (a) and (b)
→
If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A, A^2 + B^2$ is equal to$:$
→
The vector in the direction of the vector $\hat{i}-2 \hat{j}+2 \hat{k}$ that has magnitude 9 is
→