1. (a) (3 points) Find the general solution of the following differential equation dzyy' =22+, >0 Sof : - Given 4 x y y' = x ty , 270. we can use the subslition y=vx In / 1 - 4 x ( v / = 2 en/ v1 - 20 4 x ( vx ) ( v'x+ V ) = x "+ ( vx ) 4 x " V 'x + Ax V = x +vic Now Consider the absolute value : 4 xV + 4 XV = $1+VY 1 - 4 XV = p- 2C, v 4 x V - V = 1 - 4XVY ( or ) 1-4xv = _0-20 Now seperate variables!- Solve V 4 x 1 - 4 x(v 1 = ( Ite 29 (or ) 1 = ( 1 - 2 2 9 ) in 4 x V = + ItPIC (or) V = + i-ezc Substitute V back! - 2 In | 1 - 4 x VN ) = - -!, +c y= x Itezc (or) y=x 1 -e-20