Differential Equations and Integrals

y(1) = 2

y(3) = 4

y(0) = 1

y(2) = 3

Homogeneous

Non-linear

Linear

Separable

Add a constant to both sides

Multiply both sides by dx

Divide both sides by y

Divide both sides by x

dy/dx = (1/x + 1) y^6

y^6 dy = (1 + x) dx

y^6 dy = (1/x + 1) dx

dy/dx = y^6 (1 + x)

6y^7

y^6/6

7y^6

y^7/7

1/x

x

x^2/2

ln|x|

By setting it to zero

By differentiating the solution

By using the initial condition

By integrating again

7

0

128

121

y^7 = ln(x) + 7x + 121

y^7 = 7 ln(x) + x + 121

y^7 = ln(x) + x + 121

y^7 = 7 ln(x) + 7x + 121

To eliminate variables

To simplify the equation

To determine the constant of integration

To find the general solution