משוואות דיפרנציאליות רגילות רבות ניתנות לפישוט לצורה:
![](data:image/png;base64,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)
נפתח ונקבל
![](data:image/png;base64,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)
שיטת פתרון זאת נקראת הפרדת משתנים.
דוגמא 1
פתור את המשוואה הדיפרנציאלית הרגילה:
פתרון
דוגמא 2 - משוואה דיפרנציאלית רגילה עם תנאי התחלה
פתור את המשוואה הדיפרנציאלית עם תנאי התחלה
![](data:image/png;base64,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)
פתרון:
![](data:image/png;base64,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)
נציב תנאי התחלה ונקבל:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAAA+CAIAAAC+zI7BAAADbUlEQVR4nO2c24GEIAxFrYuCqIdqaIZi3A9nlUB4hIfDhJyvGRcxeiE8xrvHKXDk+HYAwhREV56IrjwRXXmypa7OqOM4DmXctyOZxoa6Wn1oCz4wZD9dPTUZC9uqqzMql8acUYs+MT/wdaPspkVXZ9QBGrrVx4V3MCq0CL+hq9U14/9nnhA9+7NFV6vhBa2+6/Q+ot+XAOThBadOj1j54GDHsRqWp+qKSffUh/bk1ZT15k0LynrhjCrpGjxaZ5T/FdMVauV/c0bFndU/EAkbndFDbVMOuIcJP6+MXuc0xparraK/+lNAUDzU9X4Gdymr79NR1WB/DIWODzTi32lh0pY4a1Qko2KrrTFfCB1d8f4aVuqMNu5MqVg4korw6UQxceYOk0ZdcofB1I8Jw2OjVXhW6noXrNQ1iM4Z46Uvqq7IETJlJWFSws6a1VvnzPvrdP0k30+rAUEUdf3vrCemEJ6YYTz9ulbUgOj6nHX9cU4KHtBqMSrHV3/FBuPA58NP47bmqRy5h+K8KXnn9amprUfkBp8Sw2ObkIfDKwff87paXRoqC+scwkhRfQfPwFA8C1y36rRXYqust6yrXwJOH3Bdr3C1DtoS1jq9Y2jjHTCugc2X6vkmvPFgeTeMttiKoLrCTSg4uoTryYyuyHPAV6NPyqs9g4qXVAmV+al43g5EW2wZYNL2Hmm0uZi5wcR+kz+sRhcltPsV95u2ILF+zWhBkEpU/RqertdqqGaMqBozRdRv8uhKfDkkv2k+bgYhNLHf+xJ7ILryRHTliejKE9GVJ6IrT0RXnoiuPBFdeSK68mQDXWe+BrMs/HW9fnJkbLFC4a/rh+QvyjzZRVdrd+qtm+i6rm9uGtx0vV4O0vZ5iS52puzA7+oKzJ9AN6sPpfROKsa8omu3S5d+vd3ybshsXce4dElYrdScl4V/iFf6a7dLt5Z/z0jq/ed9oPmaG+l26d6BDEjSe0DyNbfS7dJ9x57MCYqv2YNmEOt06bbak3eG4mtupsul+449mRsUX3MzPS7dd+zJ7KD4moMCI/Nw0qXbY0/eGYqvuZkOl+479mR+kHzNrWT/J4x6/tcM5tJ9x57MDpqvuYGkS/cM9xdTLt137MnMoPqahd+A7msWfoEmX7OwPM2+ZmFpfvd3dSGH6MoT0ZUnoitP/gCd1hmF0ZR5jQAAAABJRU5ErkJggg==)
נפתח ונקבל
שיטת פתרון זאת נקראת הפרדת משתנים.
דוגמא 1
פתור את המשוואה הדיפרנציאלית הרגילה:
פתרון
דוגמא 2 - משוואה דיפרנציאלית רגילה עם תנאי התחלה
פתור את המשוואה הדיפרנציאלית עם תנאי התחלה
פתרון:
נציב תנאי התחלה ונקבל:
אין תגובות:
הוסף רשומת תגובה