The solution of the differential equation \( x^{2} \frac{d y}{d x} \cos \frac{1}{x}-y \sin \frac...

Channel:
PW Solutions
Subscribers:
456,000
Published on ● Video Link: https://www.youtube.com/watch?v=9nEcIN64P1k


Duration: 9:07
1 views
0

The solution of the differential equation \( x^{2} \frac{d y}{d x} \cos \frac{1}{x}-y \sin \frac{1}{x}=-1 \), where \( y \rightarrow-1 \) as \( x \rightarrow \infty \) is
(a) \( y=\sin \frac{1}{x}-\cos \frac{1}{x} \)
(b) \( y=\frac{x+1}{x \sin \frac{1}{x}} \)
(c) \( y=\cos \frac{1}{x}+\sin \frac{1}{x} \)
(d) \( y=\frac{x+1}{x \cos 1 / x} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09Comprehension Let \( C \) be a curve \( f(x, y)=0 \) passing through \( (1,1) \) such that it is...
2023-06-09If \( \frac{d y}{d x}=\frac{y^{3}}{e^{2 x}+y^{2}} \) and \( y(0)=1 \), then: (a) \( y^{2}=e^{2 x...
2023-06-09The solution of \( x^{2} d y-y^{2} d x+x y^{2}(x-y) d y=0 \) is (a) \( y=x+c x y e^{y^{2} / 2} \...
2023-06-09The general solution of the differential equation \( \frac{d y}{d x}=\frac{1-x}{y} \) is a famil...
2023-06-09The area of the figure bounded by a curve, the \( \mathrm{x} \)-axis and two ordinates, one of w...
2023-06-09The solution of the equation \( (y+x \sqrt{x y}(x+y)) d x-(x-y \sqrt{x y}(x+y) d y=0 \) is (a) \...
2023-06-09The solution of differential equation \( \left(x^{5}+x+2 x^{2} y\right) d y+\left(3 x^{4} y-y\ri...
2023-06-09The solution of differential equation \( x^{2}= \) \( 1+\left(\frac{x}{y}\right)^{-1} \frac{d y}...
2023-06-09Which one of the following curve represents the solution of the initial value problem \( D y=100...
2023-06-09The general solution of \( \left(\frac{1}{x}-\frac{y^{2}}{(x-y)^{2}}\right) d x+\left(\frac{x^{2...
2023-06-09The solution of the differential equation \( x^{2} \frac{d y}{d x} \cos \frac{1}{x}-y \sin \frac...
2023-06-09Solve \( \left[x \cos \frac{y}{x}+y \sin \frac{y}{x}\right] y=\left[y \sin \frac{y}{x}-x \cos \f...
2023-06-09Prove that the following pairs are orthogonal. (i) \( 16 x^{2}+y^{2}=c \) and \( y^{16}=k x \) (...
2023-06-09The equation of the curve passing through origin and satisfying the differential equation \( \fr...
2023-06-09A function \( y=f(x) \) satisfies \[ (x+1) f^{\prime}(x)-2\left(x^{2}+x\right) f(x)=\frac{e^{x^{...
2023-06-09\( \begin{array}{l}\frac{d y}{d x}=\frac{1}{x \cos y+\sin 2 y} \text { or } \frac{d x}{d y}=x \c...
2023-06-09Solve: \( \frac{x d x-y d y}{x d y-y d x}=\sqrt{\frac{1+x^{2}-y^{2}}{x^{2}-y^{2}}} \)
2023-06-09Find solution \[ (x d y-y d x) \cdot y \sin \left(\frac{y}{x}\right)=(y d x+x d y) \cdot x \cos ...
2023-06-09Find solution \( t\left(1+t^{2}\right) d x=\left(x+x t^{2}-t^{2}\right) d t ;\left.x\right|_{t=1...
2023-06-09Find the curve such that the ordinate of any of its point is the proportional mean between the a...
2023-06-09Find solution \( \frac{d y}{d x}=\frac{y}{x}+\tan \frac{y}{x} ; y(1)=\frac{\pi}{2} \)