3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0, y(0) = 2, y'(0) = 5 12% dx +36y= 0, y(0) = 1, y'(0) = 2

Q: c. y' - y cos t = cos t %|

A:

Q: Solve the following differential equations: ylnx(dy/dx) = ((y + 1)/x)^(2)

A: Given the differential equation :ylnx(dydx​)=(xy+1​)2 The given differential equation can be written…

Q: Solve the differential equation given below 3y2(dy/dx)+y3=e-x

A: We have to solve given differential equation:

Q: Solve this differential equation: dy/dx=y/x+√(1+y/x ) ; when x=1,y=8

A:

Q: x" (t) + x'(t) – 6x = te-tcos2t %3D

A: We use the method of undetermined coefficients to find the particular solution.

Q: 2ydx = (x2 – 1)(dx – dy)

A:

Q: d) Solve the differential equation of y"" + 4y' = sec 2x

A:

Q: d’y (b) dx + y =: dx 1+x

A:

Q: Solve the differential equation 2x dy/dx + y = 2x0.5

A:

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.