Ex 95, 6 Show that the given differential equation is homogeneous and solve each of them 𝑥 𝑑𝑦−𝑦 𝑑𝑥=√(𝑥^2𝑦^2 ) 𝑑𝑥 Step 1 Find 𝑑𝑦/𝑑𝑥 x dy − y dx = √(𝑥^2𝑦^2 ) dx x dy = √(𝑥^2𝑦^2 ) dx y dx x dy = (√(𝑥^2𝑦^2 )𝑦) dx 𝑑𝑦/𝑑𝑥 = (√(𝑥^2 𝑦^2 ) 𝑦)/𝑥 Step 2 Put 𝑑𝑦/𝑑𝑥 =
Solution of y(4x+y)dx-2(x^2-y)dy=0- x=2yCy^2 ydx = 2(xy)dy dx/dy = (2(xy))/y dx/dy (2(xy))/y = 0 x' 2/y*x 2 = 0 Let x=u*v => x'=u'vv'u u'vv'u2/yuv2 = 0 v(u'2/yu)v'u2 = 0 u'2/yu= 0 (du I'm at the beggining of a differential equations course, and I'm stuck solving this equation $$(x^2y^2)dx2xy\ dy=0$$ I'm asked to solve it using 2 different methods I proved I can find integrating factors of type $\mu_1(x)$ and $\mu_2(y/x)$If I'm not wrong, these two integrating factors are $$\mu_1(x)=x^{2} \ \ , \ \ \mu_2(y/x)=\left(1\frac{y^2}{x^2}\right)^{
Solution of y(4x+y)dx-2(x^2-y)dy=0のギャラリー
各画像をクリックすると、ダウンロードまたは拡大表示できます
 | ||
 |  | |
 | ||
 |  | |
