For any real numbers α and β, let y_ , (x), x R , be the solution of the differential…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
For any real numbers α and β, let \(y_{\alpha, \beta}(x), x \in \mathbb{R},\) be the solution of the differential equation
\(\frac{d y}{d x}+\alpha y=x e^{\beta x}, y(1)=1 .\)
Let \(S=\left\{y_{\alpha, \beta}(x): \alpha, \beta \in \mathbb{R}\right\} .\) Then which of the following functions belong(s) to the set S ?
\(\frac{d y}{d x}+\alpha y=x e^{\beta x}, y(1)=1 .\)
Let \(S=\left\{y_{\alpha, \beta}(x): \alpha, \beta \in \mathbb{R}\right\} .\) Then which of the following functions belong(s) to the set S ?
Answer
(A)
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Explanation:tion of differential equation dy dx = y + _ 0 ^ 1 ydx , y (0) = 1 is :
- The function y = f ( x ) is the solution of the differential equation d y d x + x y x^ 2 -1 = x^ 4 +2 x 1-x^…
- The differential equation representing the family of curves y^ 2 =2 c(x+ c ) , where c is a positive…
- Explanation:tion of differential equation x^ 3 d y d x =y^ 3 +y^ 2 y^ 2 -x^ 2 is
- A curve passes through the point (1, 6 ) . Let the slope of the curve at each point ( x , y ) be y x + ( y x…
- If x 2 + y 2 = 1, then
- For x ∈ R , let the function y ( x ) be the solution of the differential equation d y d x +12 y= ( 12 x )…
- The Explanation:tion of the differential equation dy dx = y x + ( y / x ) ^ ( y / x ) is
More Differential Equations questions · Browse all practice questions