Exercise
$\frac{dy}{dx}=y^2-5y+6,\:y\left(0\right)=4$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=y^2-5y+6. 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^2-5y+6}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 integral \int\frac{1}{\left(y-2\right)\left(y-3\right)}dy and replace the result in the differential equation.
Solve the differential equation dy/dx=y^2-5y+6
Final answer to the exercise
$-\ln\left(y-2\right)+\ln\left(y-3\right)=x-\ln\left(2\right)$