Exercise
$\frac{dx}{dt}=\sin\left(x+t\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dx/dt=sin(x+t). When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that x+t has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable x. Differentiate both sides of the equation with respect to the independent variable t. Now, substitute x+t and \frac{dx}{dt} on the original differential equation. We will see that it results in a separable equation that we can easily solve.
Solve the differential equation dx/dt=sin(x+t)
Final answer to the exercise
$\frac{1}{-\cos\left(x+t\right)}+\tan\left(x+t\right)=t+C_0$