From the question it is given that,
y = emx … [equation (i)]
Now, differentiate the equation (i) with respect x,
\( \dfrac{ dy}{dx}\)= memx
We know that, from equation (i) y = emx
So, applying log on both side we get,
log y = mx
m = \( \dfrac{logy}{x}\)
Now, substitute the value of m and emx is equation (i) we get,
\( \dfrac{ dy}{dx}\)=\( ( \dfrac{logy}{x})y\)
By cross multiplication we get,
x(\( \dfrac{dy}{dx}\)) = y log y
Answered by Aaryan | 1 year agoFind the particular solution satisfying the given condition \( (\dfrac{dy}{dx}) = (x – 1)\dfrac{dy}{dx} = 2x^3y\)
If the interest is compounded continuously at 6% per annum, how much worth Rs. 1000 will be after 10 years? How long will it take to double Rs. 1000?
In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?
The rate of growth of population is proportional to the number present. If the population doubled in the last 25 years and the present population is 1 lac, when will the city have population 5,00,000 ?
A population grows at the rate of 5% per year. If x=x(t) denotes the number of individuals in the population after t years, then the rate of change of x is equal to 5% of x. Form the desired differential equation . Find the time period