GATE 2024 ES – Question 33
Solve $dy/dx-x^2+e^x=0$ with y(0)=1. Find y(1),taking e=2.7,to two decimals.
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Correct answer: -0.40 to -0.30
Explanation
The derivative is $y^{\prime}=x^2-e^x$. Integrate: $y=x^3/3-e^x+C$. At0,$1=-1+C$,so C=2. At1,use the prescribed e=2.7: $y(1)=1/3-2.7+2=-.3666667$,rounded **−.37**. Substituting a more accurate e would ignore the explicit numerical instruction.