Chemical Engineering Answers

Solve the initial value problem y²y'-y^3 tanx = sin x cos² x, y(0)=1

Solve (x²D² + 4xD + 2)y= (logx/x)^2,x> 0, where D =d/dx.

Solve d²y/dx²-6 dy/dx +13y= 20e^3x cos(2x+5)

Solve d³y/dx³-2 d²y/dx²+ dy/dx=sinh.x+2019

Solve d²y/dx²+2 dy/dx+y=x sinx.

Evaluate ∫0^π\2α α sin αx dx,α>0 by using Leibniz formula.

Evaluate ∫y=0^{1}∫x=y^{2√2-y^{2}}y/2√x^{2}+y^{2}dxdy ,by clange the order of integration.

Evaluate ∬R(x-y)^{2}sin^{2}(x+y)d xdy, where R is the rhombus withsuccessive vertices at (π,0),(2π,π),(π,2t) and (0,π)

Show that the vector →{v}=(yz-1)i-z(1+x+z)j+y(1+x+2z)k is conservative and find it scalar potential function.

Evaluate the line integral of →{v}=xyi+y^{2}zj+e^{2z}k over the curve C whose parametric representation is given by x=t^{2},y=2t,z=t,0<t<1.