Exams › JEE Main › Maths
Let y = y(x) be solution of the differential equation log_e(dy/dx) = 3x + 4y, with y(0) = 0. If y(−2/3 log_e 2) = α log_e 2, then the value of α is equal to :
- -1/4
- 1/4
- 2
- -1/2
Correct answer: -1/2
Solution
The differential equation can be solved using separation of variables, leading to a solution that incorporates the initial condition. By substituting the specific value of x into the solution and simplifying, we find that α equals -1/2, which matches the given correct option.
Related JEE Main Maths questions
- For a curve that passes through the point $(4,0)$, the slope is governed by \[ \frac{dy}{dx}=\frac{y}{x}+\frac{5x}{(x+2)(x-3)}. \] If the point $(5,a)$ lies on this curve, what is the value of $a$?
- Which differential equation represents the family of all conics whose axes are aligned with the coordinate axes?
- Find the equation of the curve that satisfies \[ (xy-x^2)\frac{dy}{dx}=y^2 \] and passes through the point $(-1,1)$.
- For the differential equation \[ y=\frac{y}{x}+\frac{x}{y}, \] if its general solution is written as \[ y=\frac{x}{\log|Cx|}, \] then the function $\phi\!\left(\frac{x}{y}\right)$ is
- For the differential equation \(\dfrac{dy}{dx}=\dfrac{y f'(x)-y^2}{f(x)}\), the solution is
- The differential equation \(\sec^2 x\,\tan y\,dx+\sec^2 y\,\tan x\,dy=0\) has which general solution?
⚔️ Practice JEE Main Maths free + battle 1v1 →