CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q283 Markshomogeneous_equations
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 28 (Differential Equations)
Solve \(xy\prime=y-x\tan(y/x)\). OR Solve \(y\prime=e^{x+y}+e^{x-y}\).
Alternative 1 3 Marks
Solve \(xy\prime=y-x\tan(y/x)\).
Answer: x sin(y/x)=C on regular branches.
- Set u=y/x. Then xu′=−tan u.
- Where separation is valid, integrate cot u du=−dx/x.
- This gives x sin u=C, including the straight solutions u=nπ by C=0. The original equation requires tan u to exist.
Alternative 2 3 Marks
Solve \(y\prime=e^{x+y}+e^{x-y}\).
Answer: arctan(eʸ)=eˣ+C.
- Set u=eʸ>0.
- The equation becomes u′=eˣ(1+u²).
- Separate and integrate du/(1+u²)=eˣdx.