Let x>0. Given the following differential equations. (M):xy ′
+y=2e 2x
. 1) Write (M) in its standard form and find an integrating factor of it. 2) Find a general solution of (M). 3) Solve the IVP xy ′
+y=2e 2x
,y(1)=2. Given the following differential equations. (M):(y−6)dx+(x 2
+9)dy=0. 1) Write (M) as y ′
=f(x,y). 2) Show that f is a separable function. 3) Find an implicit solution of (M). (Hint: ∫ x 2
+a 2
1
​
dx= a
1
​
tan −1
( a
x
​
)+c ) Let x>0. Given the following differential equations. (M):xy ′
+y=2e 2x
. 1) Write (M) in its standard form and find an integrating factor of it. 2) Find a general solution of (M). 3) Solve the IVP xy ′
+y=2e 2x
,y(1)=2.