Final answer to the problem
$\frac{1}{5}\ln\left|y\right|+\frac{1}{5}\ln\left|\frac{\sqrt{2}}{\sqrt{y^2+2}}\right|=x+C_0$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Can't find a method? Tell us so we can add it.
1
Combine all terms into a single fraction with $2$ as common denominator
Learn how to solve integration by trigonometric substitution problems step by step online.
$\frac{dy}{dx}=\frac{5y^3+2\cdot 5y}{2}$
Learn how to solve integration by trigonometric substitution problems step by step online. Solve the differential equation dy/dx=(5y^3)/2+5y. Combine all terms into a single fraction with 2 as common denominator. Multiply 2 times 5. 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 \frac{2}{5y^3+10y}dy.
Final answer to the problem
$\frac{1}{5}\ln\left|y\right|+\frac{1}{5}\ln\left|\frac{\sqrt{2}}{\sqrt{y^2+2}}\right|=x+C_0$
