Download App

Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations5 Marks
Question
Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\frac{\text{x e }^\text{x}\log\text{x}+\text{e}^\text{x}}{\text{x}\cos\text{y}}$
✓

Answer

We have,$\frac{\text{dy}}{\text{dx}}=\frac{\text{x e }^\text{x}\log\text{x}+\text{e}^\text{x}}{\text{x}\cos\text{y}}$
$\Rightarrow\text{x}\cos\text{y dy}=(\text{x e}^\text{x}\log\text{x}+\text{e}^\text{x})\ \text{dx}$
$\Rightarrow\cos\text{y dy}=\Big(\text{e}^\text{x}\log\text{x}+\frac{1}{\text{x}}\text{e}^\text{x}\Big)\ \text{dx}$
Integrating both sides, we get
$\int\cos\text{y dy}=\int\Big(\text{e}^\text{x}\log\text{x}+\frac{1}{\text{x}}\text{e}^\text{x}\Big)\text{dx}$
$\Rightarrow\sin\text{y}=\log\text{x}\int\text{e} ^\text{x}\text{dx}-\int\frac{1}{\text{x}}\text{e}^\text{x}\text{dx}+\int\frac{1}{\text{x}}\text{e}^\text{x}\text{dx}$
$\Rightarrow\sin\text{y}=\text{e}^\text{x}\log\text{x}+\text{C}$
Hence, $\sin\text{y}=\text{e}^\text{x}\log\text{x}+\text{C}$ is the 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 "Solve the Following Question.(5 Marks)" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

A bag contains 4 white, 7 black and 5 red balls. Three balls are drawn one after the other without replacement. Find the probability that the balls drawn are white, black and red respectively.
→
Differentiate the following w.r.t. x:

$\left[(\tan x)^{\tan x}\right]^{\tan x}$ at $x=\frac{\pi}{4}$

→
Evaluate the following integrals:
$\int\frac{1}{\sin^4\text{x}+\sin^2\text{x}\cos^2\text{x}+\cos^4\text{x}}\ \text{dx}$
→
Evaluate the following integrals:
$\int\frac{1}{(\text{x}^2-1)\sqrt{\text{x}^2+1}}\text{ dx}$
→
If $x^m + y^n = 1,$ Prove that $\frac{\text{dy}}{\text{dx}}=-\frac{\text{my}}{\text{nx}}$
→
Using differentials, find the approximate values of the following:
$\sqrt{25.02}$
→
A shopkeeper has $3$ varieties of pens ' $A$ ',$ 'B'$ and $'C'$. Meenu purchased $1$ pen of each variety for a total of$ Rs 21.$ Jeevan purchased $4$ pens of $'A'$ variety $3$ pens of ' $B$ ' variety and $2 $ pens of ' $C$ ' variety for $Rs 60 $. While Shikha purchased $6$ pens of 'A' variety, $2$ pens of $'B'$ variety and $3$ pens of $'C'$ variety for $Rs 70 $. Using matrix method, find cost of each variety of pen.
→
Evaluate the following intregals:
$\int\frac{4\text{x}^2+3}{(\text{x}^2+2)(\text{x}^2+3)(\text{x}^2+4)}\ \text{dx}$
→
Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one-half of the original amount of radium to decompose?
→
Find the equation of the line passing through the points (-1, 2, 1) and parallel to the line $\frac{2\text{x}-1}{4}=\frac{3\text{y}+5}{4}=\frac{2-\text{z}}{3}.$
→