The document summarizes how to solve a differential equation using an appropriate transformation. It presents the steps to solve the DE dy/dx = cos(x + y + 4) by letting u = x + y + 4. This transforms the DE into an equation that can be integrated and solved for csc u - cot u = x + c. The summary concludes by thanking the audience.

1. Presentation on solve the DE by choosing appropriate transformation
Presenter :
Md. Rakib Hasan
ID:162-15-7802
B.Sc. In CSE
Daffodil International University

2. WITH RESPECT TO
Saba Fatema
Senior Lecturer
Daffodil International University

3. SOLVE THE FOLLOWING DE BY CHOOSING APPROPRIATE TRANSFORMATION:
𝑑𝑦
𝑑𝑥
= COS(𝑥 + 𝑦 + 4)
Solution:
Given,
𝑑𝑦
𝑑𝑥
= cos(𝑥 + 𝑦 + 4) −−−−− −(1)
Let,
𝑢 = 𝑥 + 𝑦 + 4
⇒
𝑑𝑢
𝑑𝑥
= 1 +
𝑑𝑦
𝑑𝑥
⇒
𝑑𝑢
𝑑𝑥
= 1 + cos 𝑢 𝑢𝑠𝑖𝑛𝑔 1
⇒
1
1 + cos 𝑢
𝑑𝑢 = 𝑑𝑥

4. ⇒
1 − cos 𝑢
1 − 𝑐𝑜𝑠2 𝑢
𝑑𝑢 = 𝑥
⇒
1 − cos 𝑢
𝑠𝑖𝑛2 𝑢
𝑑𝑢 = 𝑥
⇒
1
𝑠𝑖𝑛2 𝑢
𝑑𝑢 −
cos 𝑢
𝑠𝑖𝑛2 𝑢
𝑑𝑢 = 𝑥
⇒ csc2
𝑢 𝑑𝑢 − csc 𝑢 cot 𝑢 𝑑𝑢 = 𝑥
⇒ − cot 𝑢 + csc 𝑢 = 𝑥 + 𝑐
⇒ csc 𝑢 − cot 𝑢 = 𝑥 + 𝑐
⇒ csc 𝑥 + 𝑦 + 4 − cot 𝑥 + 𝑦 + 4 = 𝑥 + 𝑐 (𝐴𝑛𝑠)

5. THANK YOU