Stark

7. A) Solve (4𝐷4 − 8𝐷3 − 7𝐷2 + 11𝐷 + 6)𝑦 = 0 Answer:-

6. C) Find the general and singular solutions of 𝑥𝑝2 + 𝑥𝑝 − 𝑦𝑝 + 1 − 𝑦 = 0 Answer:-

6. B) Prove that the system of parabolas 𝑦2 = 4𝑎(𝑥 + 𝑎) are self-orthogonal Answer:-

6. A) Solve (x2 + y3 + 6x)dx + y2xdy = 0 Answer:-

5. C) Solve p3 + 2xp2 + y2p2 – 2xy2p = 0 Answer:-

5. B) Water at temperature 10°𝐶 takes 5 minutes to warm up to 20°𝐶 at a roomtemperature of 40°𝐶. Find the temperature of the water after 20 minutes. Answer:-

5. A) Solve dy/dx+ y tan x = y3sec x Answer:-

4. C) Find the extreme values of x3+y3-3axy , a>=0

If u = f(y-x/xy, z-x/xz), show that x² ∂u/∂x + y2 ∂

(i) lim 𝑥→0  (𝑎𝑥 + 𝑥)1/𝑥               (ii) lim 𝑥  𝜋 →𝜋/2 (tan 𝑥)tan2𝑥