Answer:
The general solution is

+ 
Step-by-step explanation:
Step :1:-
Given differential equation y(4) − 2y''' + y'' = e^x + 1
The differential operator form of the given differential equation
comparing f(D)y = e^ x+1
The auxiliary equation (A.E) f(m) = 0




The roots are m=0,0 and m =1,1
complementary function is 
<u>Step 2</u>:-
The particular equation is 
P.I = 
P.I = 
P.I = 



applying in integration u v formula

= 





again integration 
The general solution is 

+ 
Step-by-step explanation:
Hey there!
<u>Firstly </u><u>find </u><u>slope </u><u>of</u><u> the</u><u> </u><u>given</u><u> equation</u><u>.</u>
Given eqaution is: 3x + 2y = 5.......(i)
Now;


Therefore, slope (m1) = -3/2.
As per the condition of parallel lines,
Slope of the 1st eqaution (m1) = Slope of the 2nd eqaution (m2) = -3/2.
The point is; (-2,-3). From the above solution we know that the slope is (-3/2). So, the eqaution of a line which passes through the point (-2,-3) is;
(y-y1) = m2 (x-x1)
~ Keep all values.

~ Simplify it.



Therefore, the eqaution of the line which passes through the point (-2,-3) and parallel to 3x + 2y= 5 is 3x + 2y +12 =0.
<em><u>Hope </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
the first one is left and the second one is up