# First Order Differential Equation

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Here, we will learn how to solve the first order differential equation in Simulink.

The first order differential equation that we are trying to solve using Simulink is as follows −

```dy/dt = 4sin2t - 10y
```

The equation can be solved by integrating dy/dt to the following −

y(t)=∫(4sin2t - 10y(t))dt

Following are the steps to build a model for above equation.

• Pick up sine wave from sources library and change the amplitude to 4 and frequency to 2. This will give us 4sin2t.

• The integrator block will be used to show dy/dt that will give output y(t).

• The gain block will represent 10y.

• The input of step 1 and 3 will be given to step2.

• We need scope block to see the output y(t). The step 4 will be connected to the scope block.

Let us see the above steps in model as shown below − Run the block to see the following output − 