Linear equations of first order.
Solve the initial-value problem on the specified interval displaystyle{y}'-{3}{y}={e}^{{{2}{x}}}{o}{n}{left(-infty,+inftyright)}, text{with} {y}={0} text{when} {x}={0}.
Line 2021-03-08Answered
Linear equations of first order. Solve the initial-value problem on the specified interval .
From the given linear differential equation, .
Therefore, the integrating factor is given by
So that, the solution is given by
We can verify the function is the solution of the initial-value periblem since it satisfies the differential equation and the initial condition.