Найти общее решение уравнения.. Created by motorny0919. matematika-ru

Найти общее решение уравнения...

motorny0919 @motorny0919

September 2021 1 17 Report

Найти общее решение уравнения.

Answers & Comments

Miroslava227

Ответ:

$(y - {x}^{2} y)dy -(x + x {y}^{2}) dx = 0 \\ y(1 - {x}^{2} )dy = x(1 + {y}^{2}) dx \\ \int\limits \frac{ydy}{1 + {y}^{2} } = \int\limits \frac{xdx}{1 - {x}^{2} } \\ \frac{1}{2} \int\limits \frac{2ydy}{1 + {y}^{2} } = - \frac{1}{2} \int\limits \frac{( - 2x)dx}{1 - {x}^{2} } \\ \frac{1}{2} \int\limits \frac{d(1 + {y}^{2} )}{1 + {y}^{2} } = - \frac{1}{2} \int\limits \frac{d(1 - {x}^{2}) }{1 - {x}^{2} } \\ \frac{1}{2} ln(1 + {y}^{2} ) = - \frac{1}{2} ln(1 - {x}^{2} ) + ln(C) \\ ln(1 + {y}^{2} ) = - ln(1 - {x}^{2} ) + ln(C) \\ ln(1 + {y}^{2} ) = ln( \frac{C}{1 - {x}^{2} } ) \\ {y}^{2} + 1 = \frac{C}{1 - {x}^{2} } \\ {y}^{2} = \frac{C}{1 - {x}^{2} } - 1 \\ {y}^{2} = \frac{C- (1 - {x}^{2}) }{1 - {x}^{2} } \\ {y}^{2} = \frac{C - 1 + {x}^{2} }{1 - {x}^{2} } \\ {y}^{2} = \frac{ {x}^{2} + C }{1 - {x}^{2} }$

1 votes Thanks 1

Answers & Comments

infinitives to be to have been

u a b c d e f x a c

8 3 8 4 4 8

i need help 649722266da94

1ba10691fa1c892d06ac0d85773a9b89

i need help 6494701346efa

tema metody integrirovaniya integrirovanie po chastyam primer na izobrazhenii

najti obshee chastichnyj reshenie uravneniya

proshu pomoch neodnorodny dif uravneniya ii go poryadka

vychislit integral uravnenie na fotografii

рекомендуемые вопросы

Helpful Links

Helpful Social