The substitution y=vx transforms the differential equation xdy-ydx=sqrt(x^2+y^2)dx into Option 1: dvsqrt(1+v^2)=dx/x Option 2: dvsqrt(1+v)=dx/x^2 Option 3: dv/v=dxsqrt(1+x^2) Option 4: dvsqrt(1+v^2)=dx/1+x^2

The answer is 'dvsqrt(1+v^2)=dx/x'. View full solution:

CUET Mathematics - The substitution y=vx transforms the differential equation xdy-ydx=sqrt(x^2+y^2)dx into | PYQs + Solutions

CUET Mathematics 2026 29th May Shift 1

Calculus

Medium

core

$\dfrac{dv}{\sqrt{1+v^2}}=\dfrac{dx}{x}$

$\dfrac{dv}{\sqrt{1+v}}=\dfrac{dx}{x^2}$

$\dfrac{dv}{v}=\dfrac{dx}{\sqrt{1+x^2}}$

$\dfrac{dv}{\sqrt{1+v^2}}=\dfrac{dx}{1+x^2}$

✅ Correct Option: 1