Differential Equations Answers

y'' − y' + 1/4 y = 8 + e^x/2

1. ysin 2x dx-dy-y^2dy-cos^2xdy=0

In a chemical manufacturing plant, a certain type of chemical B is produced

through reactions in chemical A. Through observation the officers on duty have

noted that the rate of conversion from chemical A to B is proportion to the

amount of chemical A present at any time, further investigation has revealed

that 10% amount has been converted in first five minutes.

a) The plant manager wishes to know the percentage of chemical A that will

be converted in 20 minutes.

b) The plant manager wishes to know the time it will take to convert 60

minutes of chemical A.

Determine the order and degree of the differential equation

1. y"+y"" = siny
2. x d^3y/dx^3 + 7 dy/dx - 7y = 0

Solve : 

(D² + 5DD' + 5D'²) z = x sin (3x — 2y)

y"+3y=0 , y(0)=0 and y'(3)=0

a.

cos(x)y'+sin(x)y=2cos^3(x)sin(x)-1 y(π/4)=3√2, 0<=x< π/2

b.

2xy-9x^3+(2y+x^2+1)dy/dx=0 y(0)=-3

c.

y'+4/x y=x^3y^2

DX/x+y=dy/x+y=DX/-(x+y+2z)

2ty/t^2+1 -2t(2-ln(t^2+1))y'=0​

5. (x + 2y − 1)dx − (2x + y − 5)dy = 0