Note WeBWorK will interpret acos ( x ) as cos 1 ( x ) , so in order to write a times cos ( x ) you need to type a cos ( x ) or put a space between them The general solution of the homogeneous differential equation y 1 y 0 can be written as yc acos ( x ) bsin ( x ) where a , b are arbitrary constants and yp e 1 x is a particular solution of the nonhomogeneous equation y 1 y 2 ex By superposition, the general solution of the equation y 1 y 2 ex is y yc yp so y NOTE you must use a , b for the arbitrary constants Find the solution satisfying the initial conditions y ( 0 ) 1 , y ( 0 ) 0 y The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions cos ( 1 x ) and sin ( 1 x ) of the homogeneous equation is W

Question

Note WeBWorK will interpret acos ( x ) as cos 1 ( x ) , so in order to write a times cos ( x ) you need to type a cos ( x ) or put a space between them The general solution of the homogeneous differential equation y   1 y   0 can be written as yc   acos ( x )   bsin ( x ) where a , b are arbitrary constants and yp   e 1 x is a particular solution of the nonhomogeneous equation y   1 y   2 ex By superposition, the general solution of the equation y   1 y   2 ex is y   yc   yp so y   NOTE  you must use a , b for the arbitrary constants Find the solution satisfying the initial conditions y ( 0 )   1 , y ( 0 )   0 y   The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions cos ( 1 x ) and sin ( 1 x ) of the homogeneous equation is W

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Note WeBWorK will interpret acos ( x ) as cos 1 ( x ) , so in order to write a times cos ( x

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