Question

Need help on 8,9 and 10 please.

(1 point) Use substitution to find the general solution of the differential equation (7x - y)dx +ady 0 (Use C to denote the arbitrary constant and In input | if using In.) help (formulas) Solve the differential equation (y2 + xy) dx-x2 dy = O c- Inlx G-loves Solve the homogeneous differential equation -yd(xaydy0 Note: Some algebraic manipulation goes into putting your answer into the form below. 10% of the following is a solution to the IVP consisting of the homogeneous equation -ydx +(x +vy dy 0 with the initial condition y(4) 1. (Note: Some algebraic manipulation goes into putting your answer into the form below.)

Answer 1

" Because (y^2 + ny) dx - x^2 dy = 0 (y^2 + xy) dx = x^2 dy y^2 + xy/x^2 = dy/dx (y/x)^2 + (y/x) = dy/dx let y/x = t y = tx dy/dx = 1. 1 + x. dt/dx t^2 + t = t + x dt/dx t^2 = x dt/dx dx/x = dt/t^2