Final answer to the problem
$v=-1+\sqrt{2s+\ln\left(s^2\right)+C_1+1},\:v=-1-\sqrt{2s+\ln\left(s^2\right)+C_1+1}$
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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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1
Factoring by $s$
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$\frac{dv}{ds}=\frac{s+1}{s\left(1+v\right)}$
Learn how to solve problems step by step online. Solve the differential equation dv/ds=(s+1)/(sv+s). Factoring by s. Group the terms of the differential equation. Move the terms of the v variable to the left side, and the terms of the s variable to the right side of the equality. Simplify the expression \left(s+1\right)\frac{1}{s}ds. Integrate both sides of the differential equation, the left side with respect to v, and the right side with respect to s.
Final answer to the problem
$v=-1+\sqrt{2s+\ln\left(s^2\right)+C_1+1},\:v=-1-\sqrt{2s+\ln\left(s^2\right)+C_1+1}$
