GATE 2016 ME (ME1) – Question 37
If $y=f(x)$ satisfies $y^{\prime\prime}+9y=0$, $y(0)=0$, $y(\pi/2)=\sqrt2$, then $y(\pi/4)$ is ______.
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Correct answer: -1.05 to -0.95
Explanation
The general solution of y-double-prime+9y=0 is A cos3x+B sin3x. Condition y(0)=0 gives A=0; y(π/2)=sqrt2 gives−B=sqrt2. Hence y(π/4)=−sqrt2 sin(3π/4)=**−1**. Both boundary conditions are required to fix the constants.