Question

 By using the method of variation of parameter, find the general solution of the differential equation:

 

equation

04 Sep 2025
Answer :
Word Count : 92
The complementary (homogeneous) equation $y''+y=0$ has solutions $y_1=\cos x,\;y_2=\sin x$, so $y_c=C_1\cos x+C_2\sin x$. Use variation of parameters for $y''+y=\sec^2x$. The Wronskian $W=y_1y_2'-y_1'y_2=\cos _________ _____ _______ _______ _____ _____ __________.
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