Exercise
$y'=y+y\:^2,\:y\left(0\right)=0.5$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=y+y^2. Rewrite the differential equation using Leibniz notation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{y+y^2}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation y^'=y+y^2
Final answer to the exercise
$\ln\left(y\right)-\ln\left(y+1\right)=x+\ln\left(0.5\right)-\ln\left(1.5\right)$