Differential Equations Answers

Find the general solutions of the following differential equations using D-operator methods:

2.1 (D² - 2D + 5)y = x+5

2.2 (D+4)² x = sinh4t

The expression that is equivalent to (a3b2)3 is

Solve 𝑧𝑝 = −𝑥.

45) Find the integral surface of the equation x(y ^ 2 + z) * p - y(x ^ 2 + z) * q = (x ^ 2 - y ^ 2) * z whic the straight line x + y = 0, z = 1

(D^3+1) y= 3+e^(-x) +5e^2x?

solve px+qy=y

-3x + (D+2)y=e^-t

Solve the differential equation (x +4) dy/dx = x(y-3), given that y=4 when x= -3.

Given that y_1 = e^{x}

y1 =e^x

is a solution of xy’’+(1-2x)y’+(x-1)y=0

xy’’+(1−2x)y’+(x−1)y=0, find its second solution y_2

y2

(0,∞), which is linearly independent from y1

Use any appropriate method in finding the indicated solution of the following differential 

equations. 

[2𝑥𝑦 cos(𝑥2) − 2𝑥𝑦 + 1]𝑑𝑥 + [𝑠𝑖𝑛(𝑥2) − 𝑥2]𝑑𝑦 = 0