Let \( u(x) \) and \( v(x) \) satisfy the differential equations \( \frac{d u}{d x}+p(x) u=f(x) ...

Channel:
PW Solutions
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=r1-rRJU7I6M


Duration: 12:51
1 views
0

Let \( u(x) \) and \( v(x) \) satisfy the differential equations \( \frac{d u}{d x}+p(x) u=f(x) \) and \( \frac{d v}{d x}+p(x) v=g(x) \), where \( p(x), f(x) \) and \( g(x) \) are continuous functions. If \( u\left(x_{1}\right)v\left(x_{1}\right) \) for some \( x_{1} \) and \( f(x)g(x) \) for all \( xx_{1} \), prove that any point \( (x, y) \) where \( xx_{1} \) does not satisfy the equations \( y=u(x) \) and \( y= \) \( v(x) \)
πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09Consider the following statements: According the Werners theory. A. Ligands are connected to the...
2023-06-09Match the Column-I with Column-II. \begin{tabular}{|l|l|c|l|} \hline \multicolumn{2}{|c|}{ Colum...
2023-06-09Let \( y=y(x) \) be the solution curve of the differential equation \( \frac{d y}{d x}+\left(\fr...
2023-06-09A country has food deficit of \( 10 \% \). Its population grows continuously at a rate of \( 3 \...
2023-06-09If \( y(x) \) is the solution of the differential eqution \( x d y-\left(y^{2}-4 y\right) d x=0 ...
2023-06-09\( A \) and \( B \) are two separate reservoirs of water. Capacity of reservoir \( A \) is doubl...
2023-06-09If the solution curve of the differential equation \( \frac{d y}{d x}=\frac{x+y-2}{x-y} \) passe...
2023-06-09Match the Column-I with Column-II. \begin{tabular}{|l|l|c|l|} \hline \multicolumn{2}{|c|}{\( \be...
2023-06-09The formula of dichlorobis (urea) copper (II) is: (1) \( \left[\mathrm{Cu}\left\{\mathrm{O}=\mat...
2023-06-09Let the solution curve of the differential equation \( x d y=\left(\sqrt{x^{2}+y^{2}}+y\right) d...
2023-06-09Let \( u(x) \) and \( v(x) \) satisfy the differential equations \( \frac{d u}{d x}+p(x) u=f(x) ...
2023-06-09Let the solution curve \( y=y(x) \) of the differential equation \( \left(1+e^{2 x}\right)\left(...
2023-06-09A spherical rain drop evaporates at a rate proportional to its surface area at any instant \( t ...
2023-06-09Let \( y=(x) \) and \( y=y^{2}(x) \) be two distinct solution of the differential equation \( \f...
2023-06-09Let the solution curve \( y=f(x) \) of the differential equation \( \frac{d y}{d x}+\frac{x y}{x...
2023-06-09Find the equation(s) of curved mirror \( y=f(x) \) passing through \( (8,6) \) having the proper...
2023-06-09Let \( y=y(x) \) be the solution curve of the differential equation \( \frac{d y}{d x}+\frac{1}{...
2023-06-09Let a curve \( y=y(x) \) pass through the point \( (3,3) \) and the area of the region under thi...
2023-06-09Let \( y=y(x) \) be the solution of the differential equation \[ \frac{d y}{d x}=\frac{4 y^{3}+2...
2023-06-09If the solution curve \( y=y(x) \) of the differential equation \( y^{2} d x+\left(x^{2}-x y+y^{...
2023-06-09Let a smooth curve \( v=f(x) \) be such that the slope of the tangent at any point \( (x, y) \) ...