Solve the differential equation y zx 2x y2 0SolutionTo s

Solve the differential equation: y\" + zx + (2x + y)^2 = 0

Solution

To solve this equation we have to assume \'y\' so

Assuming Y = Ae^3x

for this Y\'= 3Ae^3x

and Y\'\' = 9Ae^3x

substituting this in the equation we get

9Ae^3x + 2X + (2X+Ae^3x)^2 = 0

9Ae^3x + 2X + (2X^2 + 4XAe^3x + A^2e^6x) = 0

2X^2 + 9Ae^3x +(2 + 4Ae^3x ) X + A^2e^6x = 0

from this we can find out A value on substituting these values in the assumed equation y we will obtain the

required solution.

So, it depends on the value given in Y depending on that on taking derivartive i.e., Y\' and Y\'\' then on

substituting those values in the given equation we can get the required solution.