In this problem you will solve the non homogeneous differential equation. y"+16y=sec2(4x) n-homogeneous differential equation y"+16y sec"(4x) on the interval -7/8

In this problem you will solve the non homogeneous differential equation.

y"+16y=sec²(4x)

Extracted text: n-homogeneous differential equation y"+16y sec"(4x) on the interval -7/8<>< t/8.="" (1)="" let="" c1="" and="" c2="" be="" arbitrary="" constants.="" the="" general="" solution="" of="" the="" related="" homogeneous="" differential="" equation="" y"="" +="" 16y="0" is="" the="" function="" y,="" (x)="C" y1(x)="" +="" c2="" y2="" (t)="C1" +c2="" (2)="" the="" particular="" solution="" y,="" ()="" to="" the="" differential="" equation="" y"="" +="" 16y="sec2(4x)" is="" of="" the="" form="" yp(x)="Y1(x)" u1(x)="" +="" y2(x)="" u2(x)="" where="" u="" (x)="and" u,="" (x)="(3)" it="" follows="" that="" u1="" (x)="and" u2(x)="thus" yp(x)="(4)" therefore,="" on="" the="" interval="" (-1/8,="" 7/8),="" the="" most="" general="" solution="" of="" the="" non-homogeneous="" differential="" equation="" y"="" +="" 16y="sec2(4x)" is="" y="C1">