أجد الحل الخاص للمعادلة (dy)/(dx)=e^x-y الذي يحقق y(0)=2.

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

أجد الحل الخاص للمعادلة $\frac{dy}{dx}=e^{x-y}$ الذي يحقق $y(0)=2$ .

المعادلات التفاضلية

The answer

نكتب

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

، ثم نفصل:

e^y\,dy=e^x\,dx

. بالتكامل:

e^y=e^x+C

. نعوض

x=0,y=2

:

e^2=1+C

، إذن

C=e^2-1

. الحل الخاص

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

.

Explanation

مثال يستعمل قوانين الأسس لفصل المتغيرات.

Let Zaki explain it another way

The answer above is completely free. When you sign in, Zaki can explain this question a different way, give you ten more like it on the same lesson, and track your progress in the subject.

Practise more like this

Keep going

All Mathematics questions Mathematics hub Official past papers

Sign up now and plan your post-results step with Zaki — no invented ministry dates.

Start with Zaki Start with Zaki