Convert Volterra Integral Equation to ODE | Example 2

Converting Volterra Equation to an ODE
In this section we will present the technique that converts Volterra integral equations of
the second kind to equivalent differential equations. This may be easily achieved by
applying the important Leibniz Rule for differentiating an integral. It seems reasonable
to review the basic outline of the rule.
This can be easily achieved by differentiating both sides of the
integral equation, noting that Leibniz rule should be used in differentiating the integral as
stated above. The differentiating process should be continued as many times as needed
until we obtain a pure differential equation with the integral sign removed. Moreover,
the initial conditions needed can be obtained by substituting x = 0 in the integral
equation and the resulting integro-differential equations as will be shown.

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Integral equations to Ordinary differential equation
Volterra Integral equation to ODE
Volterra Integral equation to Ordinary Differential equation
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[muqadaskhaliq]

Sir can you give us exercise solution notes??

[danishkhan]

Sir g konsay book say pára rahy ho book ka name tô batao