помогите решить дифференциальное уравнение и найти частное решение, удовлетворяющее данным условиям: (dx/(cos^2(x)*cos(y)))+ctg(x)*sin(y)dy
y=пи,при х=пи/3
Ответы
Ответ дал:
0
Veamos...
![dfrac{dx}{cos^2xcos y}+cot xsin y; dy=0\ \
dfrac{dx}{cos^2xcos y}=-cot xsin y; dy\ \
dfrac{dx}{cos^2xcot x}=-sin ycos y; dy\ \
displaystyle
int dfrac{dx}{cos^2xcot x}=-int sin ycos y; dy\ \
int dfrac{sin x;dx}{cos^3x}=int cos y; d(cos y)\ \
-int dfrac{d(cos x)}{cos^3x}=dfrac{1}{2}cos^2 y\ \
dfrac{1}{2cos ^2x}+C=dfrac{1}{2}cos^2 y](https://tex.z-dn.net/?f=dfrac%7Bdx%7D%7Bcos%5E2xcos+y%7D%2Bcot+xsin+y%3B+dy%3D0%5C+%5C%0Adfrac%7Bdx%7D%7Bcos%5E2xcos+y%7D%3D-cot+xsin+y%3B+dy%5C+%5C%0Adfrac%7Bdx%7D%7Bcos%5E2xcot+x%7D%3D-sin+ycos+y%3B+dy%5C+%5C%0Adisplaystyle%0Aint+dfrac%7Bdx%7D%7Bcos%5E2xcot+x%7D%3D-int+sin+ycos+y%3B+dy%5C+%5C%0Aint+dfrac%7Bsin+x%3Bdx%7D%7Bcos%5E3x%7D%3Dint+cos+y%3B+d%28cos+y%29%5C+%5C%0A-int+dfrac%7Bd%28cos+x%29%7D%7Bcos%5E3x%7D%3Ddfrac%7B1%7D%7B2%7Dcos%5E2+y%5C+%5C%0Adfrac%7B1%7D%7B2cos+%5E2x%7D%2BC%3Ddfrac%7B1%7D%7B2%7Dcos%5E2+y "dfrac{dx}{cos^2xcos y}+cot xsin y; dy=0\ \
dfrac{dx}{cos^2xcos y}=-cot xsin y; dy\ \
dfrac{dx}{cos^2xcot x}=-sin ycos y; dy\ \
displaystyle
int dfrac{dx}{cos^2xcot x}=-int sin ycos y; dy\ \
int dfrac{sin x;dx}{cos^3x}=int cos y; d(cos y)\ \
-int dfrac{d(cos x)}{cos^3x}=dfrac{1}{2}cos^2 y\ \
dfrac{1}{2cos ^2x}+C=dfrac{1}{2}cos^2 y")
![boxed{cos^2 y=sec^2x+K}\ \
cos^2 (pi /3)=sec ^2(pi)+K\ \
dfrac{1}{4}=1+Kto K=-dfrac{3}{4}\ \ \
boxed{cos^2 y=sec^2x-dfrac{3}{4}}\ \](https://tex.z-dn.net/?f=boxed%7Bcos%5E2+y%3Dsec%5E2x%2BK%7D%5C+%5C%0Acos%5E2+%28pi+%2F3%29%3Dsec+%5E2%28pi%29%2BK%5C+%5C%0Adfrac%7B1%7D%7B4%7D%3D1%2BKto+K%3D-dfrac%7B3%7D%7B4%7D%5C+%5C+%5C%0Aboxed%7Bcos%5E2+y%3Dsec%5E2x-dfrac%7B3%7D%7B4%7D%7D%5C+%5C%0A "boxed{cos^2 y=sec^2x+K}\ \
cos^2 (pi /3)=sec ^2(pi)+K\ \
dfrac{1}{4}=1+Kto K=-dfrac{3}{4}\ \ \
boxed{cos^2 y=sec^2x-dfrac{3}{4}}\ \")
Похожие вопросы
2 года назад
2 года назад
7 лет назад
9 лет назад
9 лет назад