Question: In Problems 1-30, solve the equation.
Definition of Initial Value Problem: By an initial value problem for an nth-order differential equation we mean: Find a solution to the differential equation on an interval I that satisfies at x0 the n initial conditions
Where and are given constants.
Homogeneous: it is satisfying only the function turns into format.
Linear coefficient: here we need to convert both the variables into another two variables. For example, x as u and y as v.
Formulae to be used:
Since the given equation is linear coefficients. So, we can take
Evaluate the equation (1).
Using the condition, we get,
Solve the above equations to find the values of h and k.
Substitute h = 3.
So, the founded equation is homogeneous.
Let us take .
Now integrate the equation (2) on both sides.
Find the value of separately.
Substitute the value here.
Again, substitute the value of s, u and v
Hence, the solution of given initial value problem is .
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