Question:medium
If \(x y' + y - e^x = 0, \, y(a) = b\), then
\[ \lim_{x \to 1} y(x) \text{ is} \]
If \(x y' + y - e^x = 0, \, y(a) = b\), then
\[ \lim_{x \to 1} y(x) \text{ is} \]
\[ \lim_{x \to 1} y(x) \text{ is} \]
Show Hint
For first-order linear differential equations, use an integrating factor to simplify and solve the equation.
Updated On: Nov 28, 2025
- \(e + 2ab - e^a\)
- \(e^2 + ab - e^{-a}\)
- \(e - ab + e^a\)
- \(e + ab - e^a, \, y' = \frac{dy}{dx}\)
Top Questions on Differential Equations
- The acceleration \( f \) (in ft/sec\(^2\)) of a particle after a time \( t \) seconds starting from rest is given by:
\[ f = 6 - \sqrt{1.2t}. \]
Then the maximum velocity \( v \) and the time \( T \) to attain this velocity are:- WBJEE - 2024
- Mathematics
- Differential Equations
- If $$ y = \tan^{-1} \left[ \frac{\log_e\left(\frac{e}{x}\right)}{\log_e(e x^2)} \right] + \tan^{-1} \left[ \frac{3 + 2\log_e x}{1 - 6\cdot\log_e x} \right], $$ then \( \frac{d^2y}{dx^2} = ? \)
- WBJEE - 2024
- Mathematics
- Differential Equations
- If a particle moves in a straight line according to the law \(x = a \sin(\sqrt{t} + b)\), then the particle will come to rest at two points whose distance is:
- WBJEE - 2024
- Mathematics
- Differential Equations
- Let \(f\) be a differential function with
\[ \lim_{x \to \infty} f(x) = 0. \text{ If } y' + y f'(x) - f(x) f'(x) = 0, \lim_{x \to \infty} y(x) = 0 \text{ then,} \]- WBJEE - 2024
- Mathematics
- Differential Equations
- Want to practice more? Try solving extra ecology questions todayView All Questions