CUET · MATHS · PYQ PAPER 2023

Solution of the differential equation \(\frac{d y}{d x}=1+x+y+x y\) are :

A \(\log (1+y)=x-\frac{x^2}{2}+C\)
B \(\log (1-y)=x+\frac{x^2}{2}+C\)
C \(\log (1-y)=x+\frac{x^2}{2}+C\)
D \(\log (1+y)=-x-\frac{x^2}{2}+C\)
where C is arbitrary constant

Verified Solution

Answer & Solution

Correct Answer

(A) \(\log (1+y)=x-\frac{x^2}{2}+C\)

Step-by-step Solution

Detailed explanation

\(\frac{d y}{d x}=(1+x)(1+y)\) \(\int \frac{d y}{1+y}=\int (1+x) d x\) \(\log (1+y)=x+\frac{x^2}{2}+C\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From CUET

Match List-I with List-II

List- I	List- II
(A) For a series LC circuit	(I) Currents in L and C are 180° out of phase
(B) For a parallel LC circuit	(II) Power Factor=0
(C) For a purely capacitive circuit	(III) Voltage across L and C are 180° out of phase
(D) For a series LCR circuit at resonance	(IV) Reactance is zero

Choose the correct answer from the options given below:

CUET 2025 Hard

Explore more questions on app