HIGHER COLLEGES oF FACUITY OF 1 Q1 ENGINEERING TECHNOLOGY S

HIGHER COLLEGES oF FACUITY OF 1.) Q1: ENGINEERING TECHNOLOGY & SciENCE solve for the MEN\'s CoLLEGE general solution of each differential equation 5pts each x+ y 5 use separable of equation

Solution

We have dy/dx = xy +5x +y +5 = x (y+5)+1(y+5)= (y+5)(x+1) so that dy/(y+5) = (x+1)dx.Hence, dy/(y+5)= (x+1)dx = xdx + dx or, ln|y+5|+c₁ = x²/2 +x +c₂, where c₁ and c are constants or, ln|y+5|+c₁ = (x²+2x)/2 +c₂ or, ln|y+5| = (x²+2x)/2+(c₂-c₁)= (x²+2x)/2+c,where c= c₂-c₁ , is a constant. Then, |y+5| = e^[(x²+2x)/2+c].