Exercise
$\left(y-1\right)dy=\left(3x^2+4x+2\right)dx$
Step-by-step Solution
Learn how to solve definition of derivative problems step by step online. Solve the differential equation (y-1)dy=(3x^2+4x+2)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(y-1\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately. Expand the integral \int\left(3x^2+4x+2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Solve the integral \int ydy+\int-1dy and replace the result in the differential equation.
Solve the differential equation (y-1)dy=(3x^2+4x+2)dx
Final answer to the exercise
$y=1+\sqrt{2x^{3}+4x^2+4x+C_1+1},\:y=1-\sqrt{2x^{3}+4x^2+4x+C_1+1}$