Differential equation x dy dx =1,y(1)=0 Function y= - Vidyadip

Question

Differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=1,\text{y}(1)=0$

Function $\text{y}=\log\text{x}$

✓

Answer

Here, y = logx

Differentiating it with respect to x,

$\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$

$\text{x}\frac{\text{dy}}{\text{dx}}=1$

so, y=logx is a solution of the equation

If $\text{x}=1,\text{y}=\log1=0$

so,

y(1) = 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 "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

Evaluate the following integrals:
$\int_{0}^\limits{1}\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big)\text{dx}$

Write the angle between the lines 2x = 3y = -z and 6x = -y = -4z.

If $\text{x} = \text{a}\sin\text{t} \text{ and } \text{y = a} \bigg(\cos\text{t} + \log\tan\frac{\text{t}}{2}\bigg),\text{ find } \frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}.$

Let A = [-1, 1]. Then, discuss whether the following functions from A to itself are one-one, onto or bijective:
$\text{f(x)}=\frac{\text{x}}{2}$

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$

By using properties of determinants, show that:
$\begin{vmatrix}a-b-c&2a&2a\\2b&b-c-a&2b\\2c&2c&c-a-b\end{vmatrix}=(a+b+c)^3$

If $f : A \rightarrow B$ is a one-one onto function, then prove that :$
\left(f^{-1}\right)^{-1}=f
$

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.

Manufacturer can sell x items at a price of rupees $(5-\frac{\text{x}}{100})$ each. The cost price is Rs $\Big(\frac{\text{x}}{5}+500\Big)$. Find the number of items he should sell to earn maximum profit.

Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.