Differential Equations Answers

Express 2/y²-1 in partial fractions. Hence solve the differential equation 2xdy/dx +1 = y² given that y= -3 when x= 1, expressing y explicitly in terms of x.

Express 1 / y(y+1) in partial fractions.

Hence solve the differential equation dy/dx = y(y+1) / x given that y=4 when x=2 expressing y explicitly in terms of x.

Find the particular solution of each of the differential equation expressing y explicitly in terms of x.

e) dy/dx - 2xy = 0 y=3 when x = 0

f) xdy/dx + y ²= 0 (x>0) y=1/2 when x= 1

Find the particular solution of each of the differential equation expressing y explicitly in terms of x.

c) (x+4)dy/dx + 3 = y y=13 when x= 1

d) e^ydy/dx + sinx = 0 y=0 when x = π/2

Find the particular solution of each of the differential equation expressing y explicitly in terms of x.

a) y²dy/dx = 2x²+1 y=1 when x=1

b) xdy/dx = y+2 y=7 when x=3

Find the general solution of each differential equation, expressing y explicitly in terms of x.

3) dy/dx= 3x²(y+1)

4) dy/dx = y-1 / 2x-1

Find the general solution of each differential equation, expressing y explicitly in terms of x.

1) dy/dx = 2y

2) dy/dx = y+1 / x+2

Find the general solution of these differential equations.

7) ydy/dx =1/ √(x) 8) dy/dx = 4x√(1-y²) 9) dy/dx = x(4+y²)

A student tries to determine the heat of solution of NH4Cl in an open container at room

temperature (250), will the value obtained be less or more than the actual value? Why?

xyy''+yy'+x²y'³=0