Final answer to the problem
$-\frac{3}{2}\ln\left|y+1\right|+\frac{3}{2}\ln\left|y-1\right|=e^x\cdot x-e^x+C_0$
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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
Multiplying the fraction by $3e^{-x}$
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$\frac{3e^{-x}dy}{dx}+x=xy^2$
Learn how to solve problems step by step online. Solve the differential equation 3e^(-x)dy/dx+x=xy^2. Multiplying the fraction by 3e^{-x}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x from both sides of the equation. Factor the polynomial xy^2-x by it's greatest common factor (GCF): x.
Final answer to the problem
$-\frac{3}{2}\ln\left|y+1\right|+\frac{3}{2}\ln\left|y-1\right|=e^x\cdot x-e^x+C_0$
