Solve an Integro-Differential Equation
Solve an integro-differential equation.
In[1]:=
![Click for copyable input](assets.en/solve-an-integro-differential-equation/In_102.png)
eqn = Derivative[1][y][x] == 1 + Sin[a x] + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(x\)]\(y[
t] \[DifferentialD]t\)\);
Obtain the general solution.
In[2]:=
![Click for copyable input](assets.en/solve-an-integro-differential-equation/In_103.png)
sol1 = DSolveValue[eqn, y[x], x]
Out[2]=
![](assets.en/solve-an-integro-differential-equation/O_53.png)
Specify an initial condition to obtain a particular solution.
In[3]:=
![Click for copyable input](assets.en/solve-an-integro-differential-equation/In_104.png)
init = y[0] == -1;
In[4]:=
![Click for copyable input](assets.en/solve-an-integro-differential-equation/In_105.png)
sol2 = DSolveValue[{eqn, init}, y[x], x]
Out[4]=
![](assets.en/solve-an-integro-differential-equation/O_54.png)
Plot the solution.
In[5]:=
![Click for copyable input](assets.en/solve-an-integro-differential-equation/In_106.png)
Plot[Table[sol2, {a, -1, 4, 0.7}] // Evaluate, {x, 0, 3}]
Out[5]=
![](assets.en/solve-an-integro-differential-equation/O_55.png)