The general solution of \( x \frac{d y}{d x}+\left(\log _{e} x\right) y=x^{1-\frac{1}{2} \log _{....

Channel:
PW Solutions
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=-oebvs3KYB8


Category:
Vlog
Duration: 2:24
3 views
0

The general solution of \( x \frac{d y}{d x}+\left(\log _{e} x\right) y=x^{1-\frac{1}{2} \log _{e} x} \)
\( \mathrm{P} \)
is equal to
(1) \( y=x^{1-\frac{1}{2} \log x}+C x^{-\frac{1}{2} \log x} \)
(2) \( y \cdot x^{\frac{1}{2} \log x}=x^{\frac{1}{2} \log x}+C \)
(3) \( y=e^{\frac{(\log x)^{2}}{2}}(x+C) \)
(4) \( y=e^{\frac{1}{2}(\log x)^{2}}\left(x^{1-\frac{1}{2}(\log x)}-x^{-\frac{1}{2}(\log x)}\right)+C \)


๐Ÿ“ฒPW App Link - https://bit.ly/YTAI_PWAP
๐ŸŒPW Website - https://www.pw.live



Other Videos By PW Solutions


2024-01-21A curve passes through the point \( \left(1, \frac{\pi}{4}\right) \) and its slope at any point ....
2024-01-21The substitution \( y=z^{\alpha} \) transforms the differential equation \( \left(x^{2} y^{2}-1\....
2024-01-21Function \( y=f(x) \) satisfies the differential equation \( \sqrt{1-x^{2} y^{2}} d x=x d y+y d ....
2024-01-21If a curve \( y=f(x) \) passes through the point \( (1,-1) \) and satisfies the differential equ....
2024-01-21The general solution of the differential equation \( (1+\tan y)(d x-d y)+2 x d y=0 \), is equal ....
2024-01-21If the differential equation of the family of curve given by \( y=A x+B e^{2 x} \), where \( A \....
2024-01-21The equation to the orthogonal trajectories of the system of parabolas \( y=a x^{2} \) is....
2024-01-21General solution of the differential equation \( x^{2}\left(x+y \frac{d y}{d x}\right)+\left(x \....
2024-01-21Match the column-I with column-II \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{ Column....
2024-01-21Question If \( P=\int_{0}^{\infty} \frac{x^{2}}{1+x^{4}} d x ; \quad Q=\int_{0}^{\infty} \frac{x....
2024-01-21The general solution of \( x \frac{d y}{d x}+\left(\log _{e} x\right) y=x^{1-\frac{1}{2} \log _{....
2024-01-21Question \( \int_{-3 \pi}^{3 \pi} \sin ^{2} \theta \sin ^{2} 2 \theta d \theta \) is equal to \(....
2024-01-21Question \( \int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\cot x}} \) is \( \frac{\pi}{k} \) then ....
2024-01-21Question If \( f \) and \( g \) are defined as \( f(x)=f(4-x) \) and \( g(x)+g(4-x)=4 \), then \....
2024-01-21Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \). Then answer the following quest....
2024-01-21If \( f(x)=\int_{1}^{x} \frac{\ln t}{1+t} d t \), then....
2024-01-21Let \( f(x) \) is a continuous function for all real values of \( x \) and satisfies \( \int_{0}....
2024-01-21If \( f(x)=\int_{x}^{x^{2}}\left(t^{2}-3 t\right) d t, 2 \leq x \leq 3 \), then absolute maximum....
2024-01-21Let \( I_{n}=\int_{1}^{e^{2}}(\ln x)^{n} d\left(x^{2}\right) \). Then answer the following quest....
2024-01-21Question \( \lim _{n \rightarrow \infty} \sum_{r=1}^{r=4 n} \frac{\sqrt{n}}{\sqrt{r}(3 \sqrt{r}+....
2024-01-21Question The value of \( \int_{1}^{e}\left(\left(\frac{1}{x}-x+x \ln x\right) \sin x\right) d x ....