المعادلات التفاضلية: Mathematics Tawjihi question with answer

A Tawjihi Mathematics question (التكامل) with the answer and worked steps.

From the Tawjihi question bank: Mathematics · التكامل

للمعادلة $\frac{dy}{dx}=e^{x-y}$ و $y(0)=2$ : أ. استعمل قوانين الأسس للفصل. ب. أوجد الحل العام. ج. أوجد الحل الخاص.

المعادلات التفاضلية

The answer

أ.

e^{x-y}=e^x/e^y

، لذلك

e^y dy=e^x dx

. ب. بالتكامل

e^y=e^x+C

. ج. من

e^2=1+C

نحصل على

C=e^2-1

، فالحل الخاص

e^y=e^x+e^2-1

.

Explanation

يمتحن فصل الأسس والشرط الأولي.

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