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Differential EquationsEasyThe Wronskian & Variation of Parameters

The Wronskian & Variation of Parameters · Easy problem

To solve y′′+y=sec⁡ty''+y=\sec t by variation of parameters, write yp=u1cos⁡t+u2sin⁡ty_p=u_1\cos t+u_2\sin t, where u1′=−y2 gWu_1'=-\dfrac{y_2\,g}{W} and u2′=y1 gWu_2'=\dfrac{y_1\,g}{W} with y1=cos⁡ty_1=\cos t, y2=sin⁡ty_2=\sin t, g=sec⁡tg=\sec t. Find u1′u_1' at t=π4t=\dfrac{\pi}{4}.