DIFFERENTIAL EQUATIONS SAMPLE PROBLEMS WITH
ANSWERS
1. 𝑐𝑦 2 = 𝑥 2 + 𝑦
Ans: 2xydx – (2x2 + y) dy = 0
2. 𝑦 2 = 4𝑎𝑥
Ans: y2dx – 2xydy = 0
3. 𝑦 = 𝐴𝑒 2𝑥 + 𝐵𝑥𝑒 2𝑥
Ans: y’’ – 4y’ + 4y = 0
4. Straight lines through the fixed point (h,k); h and k not to be
eliminated.
Ans: (y – k) dx – (x - h) dy = 0
5. Parabolas with axis parallel to x-axis.
Ans: y’y’’’- 3(y’’)2 = 0