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Exercise

$\frac{dz}{dt}-\frac{z+1}{t^2+1}=0$

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation dz/dt+(-(z+1))/(t^2+1)=0. Grouping the terms of the differential equation. Multiplying the fraction by -1. x+0=x, where x is any expression. Group the terms of the differential equation. Move the terms of the z variable to the left side, and the terms of the t variable to the right side of the equality.
Solve the differential equation dz/dt+(-(z+1))/(t^2+1)=0

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Final answer to the exercise

$z=C_1e^{\arctan\left(t\right)}-1$

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