Ответы
Ответ дал:
0
ЛОДУ 1-го порядка:
![y^2-9x^2+4xyy'=0\y=tx;y'=t'x+t\t^2x^2-9x^2+4x^2t(t'x+t)=0|:x^2\t^2-9+4tt'x+4t^2=0\9-5t^2=frac{4txdt}{dx}|*frac{dx}{x(9-5t^2)}\9-5t^2=0\5t^2=9\t^2=frac{9}{5}\t=^+_-frac{3}{sqrt5}\y=^+_-frac{3x}{sqrt5}\\y=frac{3x}{sqrt5}\frac{9x^2}{5}-9x^2+frac{36x^2}{5}=0\0=0\\y=-frac{3x}{sqrt5}\frac{9x^2}{5}-9x^2+frac{36x^2}{5}=0\0=0 y^2-9x^2+4xyy'=0\y=tx;y'=t'x+t\t^2x^2-9x^2+4x^2t(t'x+t)=0|:x^2\t^2-9+4tt'x+4t^2=0\9-5t^2=frac{4txdt}{dx}|*frac{dx}{x(9-5t^2)}\9-5t^2=0\5t^2=9\t^2=frac{9}{5}\t=^+_-frac{3}{sqrt5}\y=^+_-frac{3x}{sqrt5}\\y=frac{3x}{sqrt5}\frac{9x^2}{5}-9x^2+frac{36x^2}{5}=0\0=0\\y=-frac{3x}{sqrt5}\frac{9x^2}{5}-9x^2+frac{36x^2}{5}=0\0=0](https://tex.z-dn.net/?f=y%5E2-9x%5E2%2B4xyy%27%3D0%5Cy%3Dtx%3By%27%3Dt%27x%2Bt%5Ct%5E2x%5E2-9x%5E2%2B4x%5E2t%28t%27x%2Bt%29%3D0%7C%3Ax%5E2%5Ct%5E2-9%2B4tt%27x%2B4t%5E2%3D0%5C9-5t%5E2%3Dfrac%7B4txdt%7D%7Bdx%7D%7C%2Afrac%7Bdx%7D%7Bx%289-5t%5E2%29%7D%5C9-5t%5E2%3D0%5C5t%5E2%3D9%5Ct%5E2%3Dfrac%7B9%7D%7B5%7D%5Ct%3D%5E%2B_-frac%7B3%7D%7Bsqrt5%7D%5Cy%3D%5E%2B_-frac%7B3x%7D%7Bsqrt5%7D%5C%5Cy%3Dfrac%7B3x%7D%7Bsqrt5%7D%5Cfrac%7B9x%5E2%7D%7B5%7D-9x%5E2%2Bfrac%7B36x%5E2%7D%7B5%7D%3D0%5C0%3D0%5C%5Cy%3D-frac%7B3x%7D%7Bsqrt5%7D%5Cfrac%7B9x%5E2%7D%7B5%7D-9x%5E2%2Bfrac%7B36x%5E2%7D%7B5%7D%3D0%5C0%3D0)
![frac{dx}{x}=4frac{tdt}{9-5t^2}\frac{dx}{x}=-frac{2}{5}frac{d(9-5t^2)}{9-5t^2}\intfrac{dx}{x}=-frac{2}{5}intfrac{d(9-5t^2)}{9-5t^2}\ln|x|=-frac{2}{5}ln|9-5t^2|+C\ln|x|+frac{2}{5}ln|frac{9x^2-5y^2}{x^2}|=C;y=^+_-frac{3sqrt5x}{5} frac{dx}{x}=4frac{tdt}{9-5t^2}\frac{dx}{x}=-frac{2}{5}frac{d(9-5t^2)}{9-5t^2}\intfrac{dx}{x}=-frac{2}{5}intfrac{d(9-5t^2)}{9-5t^2}\ln|x|=-frac{2}{5}ln|9-5t^2|+C\ln|x|+frac{2}{5}ln|frac{9x^2-5y^2}{x^2}|=C;y=^+_-frac{3sqrt5x}{5}](https://tex.z-dn.net/?f=frac%7Bdx%7D%7Bx%7D%3D4frac%7Btdt%7D%7B9-5t%5E2%7D%5Cfrac%7Bdx%7D%7Bx%7D%3D-frac%7B2%7D%7B5%7Dfrac%7Bd%289-5t%5E2%29%7D%7B9-5t%5E2%7D%5Cintfrac%7Bdx%7D%7Bx%7D%3D-frac%7B2%7D%7B5%7Dintfrac%7Bd%289-5t%5E2%29%7D%7B9-5t%5E2%7D%5Cln%7Cx%7C%3D-frac%7B2%7D%7B5%7Dln%7C9-5t%5E2%7C%2BC%5Cln%7Cx%7C%2Bfrac%7B2%7D%7B5%7Dln%7Cfrac%7B9x%5E2-5y%5E2%7D%7Bx%5E2%7D%7C%3DC%3By%3D%5E%2B_-frac%7B3sqrt5x%7D%7B5%7D)
Вас заинтересует
1 год назад
1 год назад
2 года назад
2 года назад
8 лет назад
8 лет назад
8 лет назад