Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
MCQ
Which of the following differentials equation has $\text{y}=\text{C}_{1}\text{e}^{\text{x}}+\text{C}_{2}\text{e}^{-\text{x}}$ as the general solution?
  • A
    $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{y}=0$
  • ✓
    $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{y}=0$
  • C
    $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{1}=0$
  • D
    $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{1}=0$
✓

Answer

Correct option: B.
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{y}=0$
We have,
$\text{y}=\text{C}_{1}\text{e}^{\text{x}}+\text{C}_{2}\text{e}^{-\text{x}}\ ...(\text{i})$
Differentiating both sides of (i) with we get,
$\frac{\text{dy}}{\text{dx}}=\text{C}_{1}\text{e}^{\text{x}}+\text{C}_{2}\text{e}^{-\text{x}}\ ...(\text{ii})$
Differentiating both sides of (ii) with we get,
$\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=\text{C}_{1}\text{e}^{\text{x}}+\text{C}_{2}\text{e}^{-\text{x}}$
$\Rightarrow \frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=\text{y}$
$\Rightarrow \frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{y}=0$

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

The values of $\theta, \lambda$ for which the following equations $\sin \theta x - cos\theta y + (\lambda +1)z = 0$; $\cos\theta x + \sin\theta\, y - \lambda z = 0$;$ \lambda x +(\lambda + 1)y + \cos\theta z = 0$ have non trivial solution, is
→
Choose the correct answer from the given four options.The area of the quadrilateral $\text{ABCD},$ where $A(0, 4, 1), B(2, 3, -1), C(4, 5, 0)$ and $D(2, 6, 2),$ is equal to:
→
If $a,b,c$ are in $A.P$., then the value of $\left| {\,\begin{array}{*{20}{c}}{x + 2}&{x + 3}&{x + a}\\{x + 4}&{x + 5}&{x + b}\\{x + 6}&{x + 7}&{x + c}\end{array}\,} \right|$ is
→
Let $f(x) = \left\{ \begin{array}{l}{x^2} + k,\;\;\;\;{\rm{when}}\;\;x \ge 0\\ - {x^2} - k,\;\;{\rm{when\,\, }}x < 0\end{array} \right.$. If the function $f(x)$ be continuous at $x = 0$, then $k =$
→
If the set $A$ contains $7$ elements and the set $B$ contains $10$ elements, then the number one$-$one functions from $A$ to $B$ is:
→
$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$ is maximum when x =
→
Function f(x) = |x| - |x - 1| is monotonically increasing when:
→
In order that the function $f(x) = {(x + 1)^{\cot \,x}}$ is continuous at $x = 0 , f(0)$ must be defined as
→
Which of the following transformation reduce the differential quation into the form $\frac{\text{du}}{\text{dx}}+\text{P}(\text{x})\text{u}=\text{Q}(\text{x})$ into the from $\frac{\text{dz}}{\text{dx}}+\frac{\text{z}}{\text{x}}\log\text{z}=\frac{\text{z}}{\text{x}^{2}}(\log\text{z})^{2}$
→
Evaluate: $\int\frac{3\text{x}^2+1}{(\text{x}^2-1)^3}\text{dx}$
→