Exercise
$\frac{dy}{dx}y=\frac{2x^2}{3}+\sqrt{x-1}$
Step-by-step Solution
Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dxy=(2x^2)/3+(x-1)^(1/2). Rewrite the differential equation. Combine \frac{2x^2}{3}+\sqrt{x-1} in a single fraction. Divide fractions \frac{\frac{2x^2+3\sqrt{x-1}}{3}}{y} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. 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.
Solve the differential equation dy/dxy=(2x^2)/3+(x-1)^(1/2)
Final answer to the exercise
$y=\sqrt{\frac{2\left(\frac{2x^{3}}{3}+2\sqrt{\left(x-1\right)^{3}}+C_0\right)}{3}},\:y=-\sqrt{\frac{2\left(\frac{2x^{3}}{3}+2\sqrt{\left(x-1\right)^{3}}+C_0\right)}{3}}$