tex]...

olgas2000 @olgas2000

August 2022 1 5 Report

Помогите, пожалуйста решить!!!!
Найдите общее решение дифференциального уравнения первого порядка.
[tex](x-y)y-x^{2} y'=0[/tex]

Answers & Comments

NNNLLL54

Verified answer

$(x-y)y-x^2y'=0\\\\y'= \frac{(x-y)y}{x^2}\; ,\; \; \; y'= \frac{xy-y^2}{x^2}\; ,\; \; \; y'= \frac{y}{x}- (\frac{y}{x})^2\\\\u= \frac{y}{x}\; ,\; \; y=ux\; ,\; \; y'=u'x+ux'=u'x+u\; \;
 \; (x'=1)\\\\u'x+u=u-u^2\\\\u'= -\frac{u^2}{x} \; ,\quad \frac{du}{dx} =-\frac{u^2}{x} \; ,\quad \int \frac{du}{u^2}=-\int \frac{dx}{x} \\\\-\frac{1}{u}=-\ln|x|+C\\\\- \frac{x}{y} =-ln|x|+C\\\\y=\frac{x}{ln|x|-C}$

2 votes Thanks 1

Answers & Comments

Verified answer

pomogite vychislit integralc0fb4a5d030dae0640752aca39cdfa60 16635

pokazhi pismenno kak obrazuetsya povelitelnaya forma edch glagolov 1sklonit s

pomogite otvetit na test 1ob urovne ekonomiki lyuboj strany sudyat a po kol32d075f667c00c43e9b850b89a0c0c73 45196

pomogite reshit neopredelennyj integralbee5ab99f109f35aca3f601451e32aa7 45849

srochno pomogite pozhalujsta reshit najdite obshee reshenie differencialno

pomogite reshit integral 1x2dx

i perevedite predlozheniya pomnite chto perevod slozhnyh form infinitiva i infini

i perepishite i perevedite predlozheniya pomnite chto perevod slozhnyh form infini685a431c71229a46efaf2028c20fcbbc 63414

i perepishite i perevedite predlozheniya pomnite chto perevod slozhnyh form infini

prochitajte tekst i pismenno otvette na vopros what problems can computers cau

рекомендуемые вопросы

Helpful Links

Helpful Social