Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS3 Marks
Question
For each of the differential equations in find the general solution:
(ex + e–x) dy – (ex – e–x) dx = 0
✓

Answer

Given: Differential equation (ex + e–x) dy – (ex – e–x) dx = 0
$\Rightarrow \ (\text{e}^\text{x} + \text{e}^{-\text{x}}) \ \text{dy} = (\text{e}^\text{x} – \text{e}^{–\text{x}}) \ \text{dx} \ $ $\Rightarrow \ \text{dy}=\Bigg(\frac{\text{e}^\text{x}-\text{e}^{-\text{x}}}{{\text{e}^\text{x}+\text{e}^{-\text{x}}}}\Bigg) \text{dx}$
Integrating both sides, $\ \int\text{dy}=\int\Bigg(\frac{\text{e}^\text{x}-\text{e}^{-\text{x}}}{\text{e}^\text{x}+\text{e}^{-\text{x}}}\Bigg)\text{dx}$
$\Rightarrow\ \text{y}=\text{log}\Big|\text{e}^\text{x}+\text{e}^{-\text{x}}\Big|+\text{c} \ \Bigg[\because\int\frac{f'(\text{x})}{f(\text{x})}\text{dx}=\text{log}\big|f(\text{x})\big|\Bigg]$

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 "3 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

Find the slopes of the tangent and the normal to the following curves at the indicated points:
$\text{y}=\sqrt{\text{x}}\ \text{at}\ \text{x}=9$
→
Find the coordinates of the foot of the perpendicular drawn from the origin.
2x + 3y + 4z - 12 = 0
→
For the following differntial equations verify that the accompanying function is a solution:
Differential equation Function
$\text{x}+\text{y}\frac{\text{dy}}{\text{dx}}=0$ $\text{y}=\pm\sqrt{\text{a}^2-\text{x}^2}$
→
Form the differential equation of the family of curves y = a sin (x + b), where a and b are arbitrary constants.
→
Evaluate the following integrals:
$\int\frac{(1+\text{x})^3}{\sqrt{\text{x}}}\text{dx}$
→
Prove the following results:
$\tan^{-1}\frac{2}{3}=\frac{1}{2}\tan^{-1}\frac{12}{5}$
→
Using the properties of determinants, prove that

$ \begin{vmatrix} \text{a + b} & \text{b + c} & \text{c + a} \\ \text{b + c} & \text{c + a} & \text{a + b} \\ \text{c + a} & \text{a + b} & \text{b + c} \end{vmatrix}=2 \begin{vmatrix} \text{a} & \text{b} & \text{c} \\ \text{b} & \text{c} & \text{a} \\ \text{c} & \text{a} & \text{b} \end{vmatrix}$.

→
Solve the following differential equations:

$2\text{x}\frac{\text{dy}}{\text{dx}}=3\text{y},\text{y}(1)=2$

→
Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
  1. {(x, y): x is a person, y is the mother of x}.
  2. {(a, b): a is a person, b is an ancestor of a}.
→
By using the properties of definite integrals, evaluate the integral $\int\limits_0^a {\frac{{\sqrt x }}{{\sqrt x + \sqrt {a - x} }}} dx$
→