Final answer to the problem
Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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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 $2\left(y+1\right)dy$
Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$
Expand the integral $\int\left(2y+2\right)dy$ 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 $\int2ydy+\int2dy$ and replace the result in the differential equation
Solve the integral $\int3x^2dx+\int4xdx+\int2dx$ and replace the result in the differential equation
Find the explicit solution to the differential equation. We need to isolate the variable $y$