Final answer to the problem
$y=\left(\frac{x^2}{-2e^{2x}}+\frac{-\frac{1}{2}x}{e^{2x}}+\frac{-1}{4e^{2x}}+C_0\right)e^{2x}$
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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
Rewrite the differential equation using Leibniz notation
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$\frac{dy}{dx}=2y+x^2+5$
Learn how to solve problems step by step online. Solve the differential equation y^'=2y+x^2+5. Rewrite the differential equation using Leibniz notation. Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=-2 and Q(x)=x^2. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$y=\left(\frac{x^2}{-2e^{2x}}+\frac{-\frac{1}{2}x}{e^{2x}}+\frac{-1}{4e^{2x}}+C_0\right)e^{2x}$
