JAMIA 2022 — Mathematics PYQ
JAMIA | Mathematics | 2022Solve the following differentialxdxdy+1=0;y(−1)=0</span></strong><strong><spanstyle="font−size:14pt;">
Choose the correct answer:
- A.
y = log |x|
- B.
y = 2 log |x|
- C.
y = log |2x|
- D.
y = -log |x|
(Correct Answer)
y = -log |x|
Explanation
Solving
The given differential equation is:
xdxdy+1=0
1. Variable Separation:
xdxdy=−1
dy=−x1dx
2. Integration:
∫dy=−∫x1dx
y=−ln∣x∣+C
3. Applying Initial Condition y(−1)=0:
0=−ln∣−1∣+C
0=−ln(1)+C
0=0+C⟹C=0
Final Result
Substituting C=0 into the general equation:
y=−ln∣x∣
Explanation
Solving
The given differential equation is:
xdxdy+1=0
1. Variable Separation:
xdxdy=−1
dy=−x1dx
2. Integration:
∫dy=−∫x1dx
y=−ln∣x∣+C
3. Applying Initial Condition y(−1)=0:
0=−ln∣−1∣+C
0=−ln(1)+C
0=0+C⟹C=0
Final Result
Substituting C=0 into the general equation:
y=−ln∣x∣