Question: In Problems 33–40, solve the equation given in: Problem 4.
The solution of the given equation is
Homogeneous differential equation is the equation of the form , where the degree of and is same.
One has to solve the equation given in problem 4, i.e.
Comparing (1) with the equation,
Here, take x as the dependent variable and t as the independent variable.
Let , where h and k satisfy,
Solving (2) and (3),
Substituting these values of x, t, dx, dt in equation (1),
which is the required homogeneous equation in u and v.
Let in equation (4)
Differentiating both sides,
Substitute this value of localid="1663929574069" in equation (4),
Separating the variables,
Integrating both sides,
Now, solve the integration part then
Now, equation (4) becomes,
Hence, the solution of given equation is .
94% of StudySmarter users get better grades.Sign up for free