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- The general solution of y" + 16y= cost is: Select one: a. y = C₁cos(4t) + C₂sin(4t)--1/17tcost b.y=C₂cos (4t) + C₂sin (4t)--1/17 Cost C.y = C₁ cos(4t) + C₂ sin(4t) + 1/15 tcost. d.y=C₁cos(4t) + C₂sin(4t) + 1/15 costIf f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229, then ∂4f ∂x2∂y∂z at (1,1,1) is equal toSuppose that y1=e^x andy2=e^-x are two solutions of a homogeneous linear DE. Explain why y3=cosh x and y4=sinh x are also solutions of the equation.
- Suppose that y1=e^x and y2=e−x are two solutions of a homogeneous linear equations. Explain why y3=cosh(x) and y4=sinh(x) are also solutions of the equation. Provide an example2- Show that: D™ amad ]1(20*/7 Z(2m+1)l x2mtzShow that y=lnx is a solution of xy’’+y’=0 on interval (0,∞) but is not a solution on interval (-∞,∞)