If y(x) is the solution of the differential equation d y d x + ( 2 x+1 x ) y=e^ -2 x …
Mathematics · JEE Main · NTA Exams — Differential Equations
If y(x) is the solution of the differential equation \(\frac{d y}{d x}+\left(\frac{2 x+1}{x}\right) y=e^{-2 x}, x>0\), where \(y(1)=\frac{1}{2} e^{-2}\), then:
- \(y\left(\operatorname{lgg}_{e} 2\right)=\log _{e} 4\)
- y(x) is decreasing in (0, 1)
- \(y\left(\log _{e} 2\right)=\frac{\log _{e} 2}{4}\)
- y(x) is decreasing in \(\left(\frac{1}{2}, 1\right)\)
Answer
(D) y(x) is decreasing in ( 1 2 , 1 )
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Water is dropped at the rate of 2 m 3 /sec into a cone of semi vertical angle of 45°. The rate at which…
- The solution of the differential equation d y d x =(3 x+y-1)^ 2 is,
- If y=y(x) is the solution of the differential equation d y d x =( x-y) ^ 2 x, x (- 2 , 2 ) , such that y(0)=0…
- The solution of differential equation (x^ 2 -y x^ 2 ) d y+ [y^ 2 +x^ 2 y^ 2 ) d x=0 is,
- The degree of the differential equation corresponding to the family of curves y = a (x + a) 2 , where a is an…
- If f^ (x)=f(x)+ _ 0 ^ 2 f(t) d t, f(0)= 4-e^ 2 3 , then function f(x) is
- If sin x is an integrating factor of the differential equation dy dx + Py = Q, then P can be
- The curve in which the portion of the tangent included between the coordinate axes is bisected at the point…
More Differential Equations questions · Browse all practice questions