Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

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Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

Learn how to solve differential equations problems step by step online.

$2\left(y+1\right)dy=\left(3x^2+4x+2\right)dx$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(3x^2+4x+2)/(2(y+1)). 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. Simplify the expression 2\left(y+1\right)dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. The integral of the sum of two or more functions is equal to the sum of their integrals.

Final Answer

$y=-1+\sqrt{\frac{1}{2}+x^{3}+2\left(x+\frac{1}{2}\right)^2+C_0},\:y=-1-\sqrt{\frac{1}{2}+x^{3}+2\left(x+\frac{1}{2}\right)^2+C_0}$
$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

Related formulas:

4. See formulas

Time to solve it:

~ 0.24 s (SnapXam)