Problems: Solve the following differential equations, 1) xy' -y = x cos.x, with y( / 2) = 7. 2) dy = (sin x.cos.x-2ycos.x)dx. Ans.: 4y 3) xyy' -XVY² +1 =xy² + y +x+1. 4) xydx +(y+1)(x² +1)dy = y²Vx²...

Extracted text: Problems: Solve the following differential equations, 1) xy' -y = x cos.x, with y( / 2) = 7. 2) dy = (sin x.cos.x-2ycos.x)dx. Ans.: 4y 3) xyy' -XVY² +1 =xy² + y +x+1. 4) xydx +(y+1)(x² +1)dy = y²Vx² +1.dy. dy x--2y. dx dy 5) x' sin y. dx 6) xdy -[y+xy'(1-n x)]dx =0. dy 7) + ycotx 5eCOSx with y(r/2)=-4. dx dx -[x(sec y+ tan y)-2ycos y] =0. dy 8) (1+sin y)