Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Separable Differential Equation
- Exact Differential Equation
- Linear Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
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Divide fractions $\frac{1}{\frac{1}{2\left(y+1\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$
Integrate both sides of the differential equation, the left side with respect to
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 $y$