MHT CET · Maths · Differential Equations
The particular solution of the differential equation \(\cos \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=0.5, \mathrm{y}=1\) at \(x=0\) is
- A \(\cos \left(\frac{2}{x}\right)=1\)
- B \(\cos \left(\frac{y}{x-1}\right)=0.5\)
- C \(\cos \left(\frac{y-1}{x}\right)=0.5\)
- D \(\cos \left(\frac{y}{x}\right)=0.5\)
Answer & Solution
Correct Answer
(C) \(\cos \left(\frac{y-1}{x}\right)=0.5\)
Step-by-step Solution
Detailed explanation
\(\frac{\mathrm{dy}}{\mathrm{dx}} = \arccos(0.5) = \frac{\pi}{3}\) \(\int \mathrm{dy} = \int \frac{\pi}{3} \mathrm{dx}\)
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